How do I stop animals like wolves, eagles, bear from starvation?

I'd have to agree with @Pierre-Luc.
After doing some easy googling for you, I looked at the raw-files for Wolf, Eagle and Bear, and they all lack the [STANDARD_GRAZER] token. The wiki page about Black bears even states specifically: Bears in general lack the [GRAZER] tag which means they don't require pastures. This makes them an ideal component of a meat industry.

Did these animals die from wounds, or perhaps some other reason?

Animals stored in cages, as long as they are "non-grazing" (for example wolves), can stay alive without being fed. See:

http://dwarffortresswiki.org/index.php/v0.34:Captured_creatures

for details on caged creatures.