Modified from two earlier answers here and here.

Both of these groups were among the losers of the reunification process. The new German state cashiered the GDR's 91000 employees of Ministerium für Staatssicherheit (MfS, aka Stasi) and they lost their elite status. The Nationale Volksarmee (NVA) weathered reunification slightly better, with some accepted some 20000 NVA personnel reserved for the Armee der Einheit (Army of Unity). Yet, for both groups found little space for them within the new unified German state.

In the case of the NVA, the enlisted and officers had to continue their military career on terms dictated to by Bonn and the Bundeswehr. The latter element was especially problematic as the Bundeswehr was one of the bastions of anticommunism in the FRG and its commanding officers saw the NVA as a morally compromised and un-German force. The majority of the troops in the Armee der Einheit were specialists or other individuals that could maintain the little Soviet equipment that Bundeswehr elected to keep. NVA officers above Oberstleutnant were particularly not welcome in the new German army as the Bundeswehr felt that these individuals had been ideologically compromised by the regime. Evidence of MfS collaboration also became grounds for dismissal and the end of their careers. The NVA was very top-heavy in terms of officers, with an officer to enlisted ratio of 1:8, whereas the Bundeswehr maintained a ratio of 1:40. As such, the few NVA officers that remained in the Bundeswehr were dropped to the enlisted ranks as the Bundeswehr establishment saw NVA officers as performing the same functions as a Bundeswehr NCO. By about 2002, only about 5 percent of the Bundeswehr consisted of former NVA personnel. The Kohl government had both domestic and international rationales to pare down the unified military. One of the concessions Kohl paid for reunification in the 2+4 treaty that sanctified reunification was a limitation on the new German military. This concession gave Kohl leverage on other issues when negotiating with the former Allied powers. Furthermore, it became increasingly obvious to Bonn that the costs of reunification and integration of the GDR were going to be quite high. The political and actual costs of keeping both a largely obsolete GDR military establishment and its personnel were too high for Bonn's taste.

While the NVA found itself cashiered and winnowed away, the MfS feared that in addition to forced retirement, there was pressure to prosecute MfS officials for their actions. here was some attempt by the Federal Republic to prosecute various MfS agents for crimes committed under the auspices of the GDR, but they generally fizzled out. The example of foreign intelligence head Markus Wolf is instructive for how trials of MfS figures proceeded. The lower German courts convicted Wolf for treason, torture and other violations of civil liberties, but the Bundesgerichtshof (German Federal Court of Justice) overturned the conviction on the basis that Wolf was acting on behalf of a sovereign power at the time. Likewise, the FRG tried to bring MfS head Ernst Mielke to task for his actions. He was convicted for the murder of two police captains in 1931 and later brought to trial for the shootings of defectors, but Mielke's advanced age and seeming senility led to a ruling that he was not fit to stand trial. As the Mielke and Wolf trials demonstrate, it was hard to bring MfS agents to trial since this brought up a tangle of legal issues. It was difficult for FRG courts to retroactively apply West German law onto these individuals and the few trials brought to court became bogged down in legal minutia of jurisdiction.

Although they were largely free from successful prosecutions, MfS employees did not weather the reunification process very well. In the early stages of reunification in early 1990, MfS General Gerhard Niebling floated a deal in which the MfS would get amnesty and some post-unification existence in exchange for promises not to interfere with the unification process and sharing all its data it had on Western governments. This deal fell through largely because of opposition from the various GDR citizen's committees and the wider hatred the bulk of the GDR 's population held for the SED's security apparatus made such an amnesty deal a dead letter.

The dissolution of the MfS was of a piece with how the FRG approached the amalgamation of the GDR's civil servant with their Western counterparts. The attitude of the FRG bureaucrats was that the large staffs and personnel that typified GDR state employment was an economic liability and needed to be cut. For civil servants in relatively innocuous fields like the the post office or academia, it was possible for an individual GDR civil servant to find work in their new unified civil service. But for civil servants in state entities closely associated with propping up the SED dictatorship, the attitude of the FRG was more intransigent. So for the MfS, continuing to ply their trade in German intelligence was not an option.

Some 1500 low-level MfS employees did transfer into the new federal police, especially the Federal Border Guard. Others found a home in the local civil service of the eastern federal states, especially as mid-level bureaucrats in unemployment offices. However, the majority of the former MfS employees ended up in the private- and semi-public sector. Some of these jobs were relatively prestigious, but other jobs like night-watchmen were an ignominious end for what had been a state elite. Although the federal government does pay their pensions (a fight that the FRG lost in court), the pay level is considerably lower than the pensions they would have received in the GDR.

Retirement and pensions were also a major bone of contention for the NVA after 1990. Up to 2005, retired NVA officers were considered Gedient in fremden Streitkräften (a veteran of foreign armed forces), by the Ministry of Defense. This was a source of much grumbling for NVA veterans as it was a status that explicitly claimed they were not German soldiers. The Ministry of Defense reclassified them as "soldiers serving not in the Bundeswehr", a status that still implies they were serving a foreign power. Nor can NVA officers officially use their retired rank as a title, außer Dienst (retired/inactive service) in official correspondence, which is a prerogative of all retired Bundeswehr officers. Beyond the sting of official non-recognition, NVA pensions in the Berlin Republic are usually less than their counterparts and many NVA officers were forced to retire several ranks lower than when they left service.

The low status and negative public perception of the MfS and NVA in unified Germany has been the source of much bitterness for veterans of both groups. Overall, institutions like the MfS or the NVA have been relatively immune from the Ostalgia trend in the former GDR. This elegiac celebration of the GDR, as exemplified by films like Goodbye Lenin, prefers to valorize aspects of daily life and the commitment of "regular" GDR citizens to issues of social justice. The NVA's unsavory association with the Grenztruppen and the Soviets in the public eye meant that it was much more difficult to apply Ostalgia to the East German military experience and the MfS has a very public reputation as lever of SED terror and control. Given this situation, many MfS and NVA veterans have formed their own special interest lobbies, such as the Joint Initiative for the Protection of the Social Rights of Former Members of the Armed Organs and the Customs Administration of the GDR (ISOR). Despite the fact that these veterans are active and vocal in the German left, but these groups are relatively socially isolated from the unified body politic. Interviews with a number of MfS and NVA veterans feel they have been unjustly scapegoated for the excesses of the SED and some individuals even liken their position in the unified Germany to that of Jews in the Weimar Republic and Third Reich- which is a gauche and rather distorted view of German history. Reunification was a bitter pill to swallow for both of these former elite groups.

Sources

Bruce, Gary. The Firm: The Inside Story of the Stasi. Oxford: Oxford University Press, 2010.

Caldwell, Peter C., and Robert R. Shandley. German Unification Expectations and Outcomes. Basingstoke: Palgrave Macmillan, 2011.

Clarke, David, and Ute Wölfel. Remembering the German Democratic Republic: Divided Memory in a United Germany. New York: Palgrave Macmillan, 2011.

Gieseke, Jens. The History of the Stasi: East Germany's Secret Police, 1945-1990. New York: Berghahn Books, 2014.

Herspring, Dale Roy. Requiem for an Army: The Demise of the East German Military. Lanham [u.a.]: Rowman & Littlefield Publishers, 1998.