The bird cage tattoo isn’t near as common as bird and wildlife tattoos themselves, but we still see a lot of these tattoos to represent specific situations where it’s a good fit.
An open/empty bird cage is often used to represent the achievement of freedom. This can be freedom from bondage (slavery), freedom from a past woe or obligation, freedom found from ending a bad relationship, etc.
A bird cage tattoo can also have objects locked inside of it, such as hearts (to represent how love can feel like a prison in an unhealthy situation), or a brain in the bird cage (to represent how narrow minded people think), etc.
The world of tattoos has many different associative meanings for designs/symbols in the world we live in.