There are two possibilities...

The first is that the Death Star trash compactor had been used so rarely, or that the station had been serviced so infrequently, that an ecosystem had begun to develop inside the trash compactor (and who knows where else in the Death Star) and a large tentacle beast had grown in this would-be womb deep inside the most destructive weapon in the galaxy.

The second is that somebody threw a tentacle monster away in the trash.