Riddle me this:
My prefix is gotten before the race starts.
My suffix will enter without pausing parts.
My infix will soften with heat, switching hearts.
I am, altogether, a place to remain.
My prefix, an asset but not as it starts.
My suffix won't enterta'n mixed ret'na parts.
My infix is crying, but back in my hearts.
I am posted out, unlike quite a domain.
What am I?
The answer has $10$ letters, and the title is also a clue.