Can a buyer still make an indemnity claim after they've already resold the business to someone else?

Often yes, though it depends on what happened to the buyer's rights under the original purchase agreement when the business was resold. If the buyer's indemnity rights against the original seller were expressly assigned to the new purchaser as part of the resale, the new purchaser would generally be the one entitled to pursue a claim going forward, and the original buyer's own standing to claim directly may be reduced or gone, depending on how that assignment was worded.

If those rights were not assigned, or were expressly retained by the original buyer, the original buyer can generally still bring a claim for their own loss, such as a reduction in the price they were able to get on the resale that is traceable to an undisclosed issue from the original purchase, provided the claim is still within the original agreement's survival period. Because this depends heavily on how both the original purchase agreement and the later resale documents were drafted, a buyer in this position should have both sets of documents reviewed together before assuming either outcome.