It's by Social Security Number. The stimulus is being done in batches. I am sure Prosper is fully aware which Social Security Numbers are in what batch.
Aside from the fact that I doubt Prosper is smart enough to make pulls on particular loans based on the expected direct deposit date based on the borrower's social security number, there are at least two significant problems with such a plan. If the borrower is married filing jointly, the direct deposit date depends on the social security number of the first person listed on the return, so Prosper would only have a roughly 50-50 chance of that being the borrower. Second, most Prosper deadbeats probably owed the IRS money or, even if due a refund, obtained a refund anticipation loan or had their tax prep fees taken from the refund. In any of these cases, the borrower would likely get a paper check, not direct deposit. According to the IRS website, no paper checks have even been mailed out yet (and even if the IRS is a few days ahead of schedule on the first batch, that only covers 10% of the social security numbers, and who knows when the borrowers will receive them and deposit them -- or if they will even be deposited into the same account used by Prosper).