these kinds of signaling problems are universal for any costly signal. for example when signaling that you are a high value mate, the signal itself implies the question why you don't already have one. being an otherwise extremely attractive partner that's single is suspicious - something else must be going on. so 'i have a girlfriend she just goes to a different school' is an optimal first-round strategy in a multi-round game, if in the second round you become conveniently single. i forget where i was going with this

unrelated: i am recently single as my former astronaut doctor partner had to go to space to heal the moon, and our relationship would not be cut short by me being sent to prison for a botched assassination hmu

@jonny well hello there, I am also not going to prison for attempted or completed violence and also recently single from a highly successful and moral life partner. (Mine died of, um, protesting.) Can I interest you in a flirting?