Did East German intelligence give much information to reunified Germany? What about agents in the field? How were they taken care of once their country stopped existing? Were they taken care of?
NB: I'm really an early modern guy, but I am German myself with somewhat of an interest in the GDR, so I think I can at least supply you with a passable answer about East German agents in West Germany until someone who properly studied this topic can give an in-depth reply.
Okay, so first I think it's important to talk about who within the East German intelligence community did the actual spying in the west. The Ministry for State Security, or Stasi for short, was an absolute behemoth with more employees (about 91,015 by 1989) than today's CIA and the NSA put together, in a country with less people than New York State. Almost every one of its various suborganisations and departments was concerned with foreign intelligence in some way, be it technical expertise, intelligence analysis or simply looking for potential assets on both sides of the wall. Most of those strings came together in the "Hauptverwaltung Aufklärung" (Main Directorate for Reconnaissance, or "HVA" for short), a 4,600-strong department tasked with conducting foreign intelligence. For most of its existence (from 1952 to 1986) it was led by Markus Wolf. Wolf was admittedly very good at his job, but I have my doubts about the decades-old descriptions of him as sort of a legendary super spy - I'm not knowledgeable enough to say for sure, but to me it always gave off the impression of western intelligence either trying to pin its own failures onto a larger-than-life opponent or the desire of the public for mysterious James-Bond-like figures.
There was also the Military Intelligence Service (Militärische Aufklärung der Nationalen Volksarmee), an about 1,100-strong unit within the East German military that was tasked with the collection and analysis of military intelligence abroad. Although it was formally independent of the Stasi, it was de facto an extension of the HVA; the Militärische Aufklärung was not only required to report to the Stasi, but the Stasi also employed a great number of undercover agents within its ranks to make sure that noone there got any ideas.
So now that we know who was in charge of espionage in Western Germany, the next question is: What do we know? And the truth is: not much. During the public unrest of late 1989, GDR citizens stormed Stasi buildings all over the country, preventing the wholesale destruction of its archives. Not so with the Militärische Aufklärung and especially the HVA, which had always seen itself as an elite within the Stasi itself: Instead of succumbing to the general confusion of the time, their employees managed to utterly destroy an enormous amount of documents. Maybe the western intelligence agencies have more information in their archives, but public scholarship can only use the remaining documents of those two departments (which doesn't amount to a whole lot, especially when it comes to its illegal work abroad) as well as hunting for hints and additional info amongst the sea of documents obtained from the rest of the Stasi (the reports of the undercover agents within the Aufklärung actually turned out to be a great source, as most of them weren't destroyed).
There is one dataset, however, that managed to capture a lot of attention after 1989. The so-called "Rosewood" documents were somehow obtained by the CIA during the early 90s (as far as I know it's still classified how exactly they managed to do that) and passed on to the German authorities in 2003, at least those documents that pertained to German nationals. They aren't official files or agents dossier per se; for the most part, they're microfilms of index cards (about 293,000 of them, to be precise) of the HVA archives. They consist of F16 and F22 index cards, as they were called by the HVA. The F16 cards registered people's names, their personal data as well as a unique registration number. The F22 cards on the other hand registered individual files and dossiers, what sort of process the files described and registration numbers connected to them, which is how we are able to connect names with process files. A big problem however is that only a part of the names recovered from the F16 cards are actually those of foreign agents; instead, the HVA also used them to store information about potential assets, people of interest and sometimes wholly fictitious people in their archives. The Rosewood documents were one of the main sources for German investigations and counter-espionage officials in the years after reunification, but they are spotty at best and need to be used with care.
Because of all this, I think it is best to take all information about the foreign espionage efforts of the GDR with a grain of salt. Keeping this in mind, it appears that by 1989 about 3,000-3,500 citizens or permanent residents of West Germany were active agents of the HVA and Aufklärung (we know for sure about 1,553 HVA agents), with may five to six hundred of them being designated as "Quellen" (sources), i.e. regularly passing on information. They assisted in gathering information about all sorts of matters that might be of interest, ranging from politics and military to cultural and industrial espionage. They also tried to clandestinely influence what happened in West Germany (e.g. supporting GDR-friendly parties and movements, discrediting those critical towards it, sowing confusion and discord amongst West German politicians, sometimes even bribing West German parliamentarians to make sure they voted a certain way etc.), sometimes abducted West German citizens that were perceived to be a danger to the socialist regime (most of the ~400 abductions we know of happened during the 50s and 60s) and sometimes even planned and conducted assassinations abroad (look up Wolfgang Welsch for a particularly spectacular case). It's absolutely possible that there are a number deaths that were in fact covert assassinations, but we'll probably never know of them. Lastly, they also tried to lay the ground for a possible escalation of the Cold War by building up a secret guerilla army in the West, mostly comprised of members of the German Communist Party (DKP) who were offered training in the east and material support in the west. Those "sleeper agents" probably numbered about 200 between 1969 to 1989.
Okay, so we've established that the intelligence agencies of the GDR did not offer up their archives and knowledge to the west after reunification, but instead tried to destroy and obfuscate as much as possible. Yet the (West) German authorities tried their best to investigate against spies and informants working for the GDR, especially after 1990.
I'm not sure how many cases were opened against HVA and Militärische Aufklärung spies altogether, but by mid-1997 it had been a bit more than 7,000: 4,171 against (former) citizens of the GDR and 2,928 against West Germans suspected of being in the GDR's employ. It could have been more, naturally, but next to the spotty information that was available, there was an unprecedented legal problem that suddenly arose: Was it really treason if HVA officers had simply done the job they were supposed to do in service of another country that had stopped existing? Markus Wolf put it succinctly in front of the judge, when he quipped in 1993: "Which country am I supposed to have betrayed?". The Federal Constitutional Court, Germany's highest court, ruled in 1995 that only West German citizens who had knowingly spied for the GDR could be subjected to charges of treason, "Geheimnisverrat" (betrayal of state secrets) and "geheimdienstliche Agententätigkeit" (working as an agent for a foreign intelligence service), whereas Stasi officers whose permanent residence had been in the GDR by 1990 were exempt, as long as their work didn't entail additional crimes like murder or abduction. Due to this, but also because of the lack of information, the fact that many agents hadn't actually been able to gather and pass on a lot of information and finally an interest by the unified German government to not cause any more troubles amongst its 16 million new citizens than necessary meant that out of the roughly 7,000 official investigations I mentioned earlier, only 275 ended in an actual sentence. Markus Wolf for example could only be sentenced because of several cases of potential assets being captured and locked away for a time in order to force their cooperation during the late 50s.
So, what happened to those former spies that didn't end up in jail, i.e. the vast majority? Well, most were able to keep on leading their lives in peace. I can't find any additional sources confirming this from where I am right now, but it seems that the Militärische Aufklärung was transferred into the Bundeswehr with at least some of its personnel after 1990, so it might well be that GDR soldiers tasked with spying on their country's most important enemy ended up working for exactly that. Markus Wolf claimed that 90% of the HVA's foreign assets were located in West Germany, so if we assume that to be true this would mean that only a small number of agents outside of Germany had to cope with their employer suddenly ceasing to exist.
Sources:
Is it also true that there is an archive where people can look up collaborators with the Stasi within the GDR? I vaguely recall reading about it and it can destroy families to find out their own members were spying on them for the Stasi.