[Tomisimo]

Yes, I hear you. Reflexive verbs really can be confusing. And with this verb it's even more confusing, because both "quedar" and "quedarse" can mean "to stay" Often times you can use either one (I think it changes from region to region). (Él) se quedó atrás, (Él) quedó atrás. I'm not sure if there's any subtle difference between those two. To me it sounds more natural to say "me quedo", "te quedaste sin dinero" etc. as a reflexive verb.

Then of course there are lots of other meanings for quedar that don't mean to stay:

Te queda esa chamarra? - Does that jacket fit you?
Me quedan $4 ¿Qué puedo comprar? - I've got $4 left, what can I buy?
Ella se quedó con ese muchacho - She ended up with that guy.

Maybe a native speaker can offer an opinion? (sosia, atnbueno english student etc)