Everyone, this thread has generated a lot of comments which don't meet the standards of this subreddit, and thus were removed. Please, before you make to answer the question, keep in mind our rules concerning in-depth and comprehensive responses.

Follow-up question:

How much of that information has Russia declassified? Is any of it actually available?

Howdy. This thread seems to be a graveyard...

However, there is an answer to this question and it is decidedly a lot more boring than the rest of the history of the KGB. First is trying to understand the KGB. There was many facets to its existence and it was not simply Foreign Intelligence. For our American readers, the KGB encompassed both the CIA, the FBI, US Customs, Secret Service, and US Marshals. It was a far reaching organization that had many services. This bleeds into the Fall of the Soviet Union. The KGB was massively involved in trying to keep the USSR from dissolving. With the botched coup in Vilnius in January 1991 their perceived power began to wane. They were also involved with a coup against Gorbachev to regain "order." However the coup failed and in fact hastened the end of the Communist Party's hold on Russia. With the coup failing there was quick judgement placed on the KGB, with its leader, Vladimir Kryuchkov, being imprisoned. Gorbachev quickly placed a new leader who's job was to dismantle the KGB. Which gets us to your question.

The foreign agents was part of "The First Directive." Foreign Intelligence. Of the KGB's directives it was one of the few to survive. It got placed under a new branch of Government/Administration and continued operating. The new branch was the SVR, or Foreign Intelligence Service. Therefore its agents in the field would have kept working throughout the subsequent fall and continue to operate to this day.

However in the last days of the Soviet Union the KGB (before its dissolution) conducted a bunch of shredding and burning of documents, including its foreign offices. They were "covering" up what they had done, and that did include the names of foreign spies. Other files from the split nations of the former Soviet Union were transported back to Moscow as well.

So to end, the end of the KGB's foreign service is quite boring compared to the flaming descent of the KGB's internal divisions. The Foreign Service (First Directorate) just became a new service first for the last few months of the Soviet Union and then for the Russian Federation.

Some sources:

Lenin's Tomb: The Last Days of the Soviet Empire David Remnick

Foreign Intelligence in the 90s, SVR Website

Shaken but Not Stirred: The Tumultuous History and Resilliance of the KGB, Jamisen Rueckert, Marquette University Website