It depends on the particular bird, but some species will sit on eggs, even to the point of their own starvation. "Broody" is the term -- referring to a general

It depends on the particular bird, but some species will sit on eggs, even to the point of their own starvation. "Broody" is the term -- referring to a general nature to sit on and nurture eggs, working themselves into an almost hypnotic state. Chinese Silkies are known for this. Buff Orpingtons are also good "hatchers." I have to go in and collect eggs, and pet on my birds to rouse them from their broody state, then force them out of the henhouse to go eat & drink. Otherwise she'll literally sit there on those eggs all day & night. After a while, the hen might break the eggs and eat them. A way to train against this is to 1) never let it happen (remove eggs promptly) so they don't develop a taste for eggs or 2) give them golf balls to sit on. Birds go through phases. Very broody for a few months, then disinterested, then back to broody, eating eggs for a while, ignoring them, etc.