Could the stock price of the target firm fall when a buyout is announced?

The price of a target company to be acquired usually goes up because a premium must be offered to incentivize shareholders to sell. Infrequently, the opposite happens. I say infrequently because I have maintained a database for 25+ years via a Thomson Reuters subscription and I rarely see it. I'd guess that if you do a Google search, you'll find some stories out there.

One possibility for a drop in price is that based on rumors, share price has run up past the acquisition price and the buy out offer is lower.

Another is that it's a stock deal and if the merger is viewed poorly, a drop in the acquirer's price values the acquisition price lower.