But events overtook the plan, the Stasi was dissolved as angry demonstrators massed outside and invaded its offices, and the new federal authority for Stasi archives inherited all the torn paper.
It amounts, says Haussler, to "the biggest puzzle in the world", estimated at between four and six hundred million pieces of paper - some no larger than a fingernail.
The authority has had a small team in Bavaria reconstructing torn documents by hand. But humans struggle to cope with the smaller fragments. At present rates, it would take centuries to reconstruct the documents.
So now the authorities are turning to technology. Computers, says Haussler, are "quicker, cheaper and can match and remember things humans can't". The particular computer taking on the task is the "ePuzzler" made by the same people who invented the mp3 player - the Fraunhofer Institute in Berlin.
Bits of torn paper of all shapes and sizes are taken out of the sacks, ironed flat, then scanned.
Each piece, however small, is given a computer file into which is entered any information about, say, paper colour, handwriting or print on it, any significant acronyms that might link it to a particular Stasi office.
Then a complex mathematical programme is brought into action matching that information and the paper's shape with other fragments from among the millions.
A technician showed me a test run, as pieces moved around a screen before finally forming a reconstructed Stasi document.
"For many years I feared that anyone on the street could take me away," she says.
She did not see her mother again for 19 years, after the fall of the Berlin Wall. But now she's hoping the reconstructed documents will explain more about how such things were possible.
"Everybody's really hoping there will be information in these documents. Of course, we can't tell how long it will take," she says.
"Even if the computer works quickly, it'll take some time for the archivists to sort everything out - but I certainly have high hopes."
And what of those who worked for the Stasi. As more emerges about their activities, and the mass of information they kept, does former Stasi colonel Gotthold Schramm have regrets?
At times, he is defiant. "You can't have collective guilt," he says. "Guilt is an individual thing."
"With hindsight, we didn't need this giant network of unofficial collaborators," he adds. "We were too worried about what might happen. We should have trusted people more."
But they did not trust the people when they were in power.
And thousands of fragmented lives, and fragmented documents, still bear powerful witness to how a secret police force spread throughout a society.