Hi VelisarusHmm ... I think "popped out" indicates a certain amount of levity.
"I had sworn not to tell her that her mother was dead, but when she persistently questioned me about the tragic accident the secret just slipped out." I put it to you that "popped out" would sound frivolous.
Thank you for the help"Slip" can be used with an object only in certain contexts.
She slipped a stitch in her knitting.
She slipped the money into her pocket. (But "The money slipped from/out of her pocket".)
If we want to say that she removed herself from Doug's embrace, we need to use a preposition—or two.
She slipped from his embrace/out of his embrace.