The only non-sentient things that eat have grazing tags in the raws. I wont get into animal-men food requirements, but the grazers right now only eat growing grass. So far as I know you can't store it.
So if I wanted to capture egg-laying grazers, I could (for example) build a series of 1-tile-wide ramp-and-tunnels down into a soil layer, clear out a 2x2 or 3x3 pasture in a soil layer, and then in the entry chute I could have
- Surface entrance
- Cage trap
- Door
- Nest Box
- 2x2 or 3x3 pasture area (as required by local creatures)
If the cage trap catches a creature going for the box, I train the creature and then release it again ASAP. It should path back to its nest box, since claiming is remote and appears semi-permanent. Once the creature sits a clutch, I can forbid the door, secure in the knowledge that the creature and its chicks will have grazing space until I need to retrieve them. I could even rig up underground access to the pasture, provided I installed another forbidden door there and wasn't worried about thieves.
Of course, a thief that tries to sneak in via a henhouse will be spotted by the mother creature, who occupies a 1x1 tile directly in the thief's path... much in the way we have used kittens in the past!
Is this a solid plan, or what?