To add a little to my reply, FeLV is spread through long-term contact. It is not highly contagious.

If you had a kitten who tested positive for FeLV, I would say DO NOT LET THEM EUTHANIZE!! It SHOULD NOT BE AN AUTOMATIC DEATH SENTENCE!! Wait three months and re-test.

Honestly, when I first read that they euthanized Gary automatically because of an FeLV test, I was pretty horrified. It's such a poorly understood disease, and cats beat it frequently enough that it should in no way mean automatic death. I've worked for three different clinics, one of them cat-only, and the wait-retest strategy was universal between the three of them.