There is nothing more badass than the tiny birds (I guess they are some sort of tits - and yes I have to chuckle about that name every time) coming to our balcony and collecting cat fur from our doormat to bolster their nest.
They also know exactly that my cat can't reach them without a human opening the door, so they seem absolutely unimpressed if she announces their upcoming demise from the other side of the window.

Good to know, if you witness birds doing the same: If you treat your pets chemically against ticks or fleas, please remove their hair from your garden/balcony. The chemicals in tick and flea treatment can negatively impact birds' breeding chances.

Edit: If you want to help your bird friends offer untreated wool, straw or jute instead.