well, I did quite a lot of reading past few days on the subject and came up with few clues.
Am_Wannabe, you don't have to be refugee to be stateless, lot of people still face this situation, trust me. For one, if you recall the breakup of USSR, you will understand why some of us can't obtain nothing from embassies. Canada for example will ussue a travel document not only for refugees but stateless also, while USA only for refugees.
To travel you need either passport or travel document where the embassies stamp their entry Visas. Looks like for GC holder with no home passport the solution is I-131 reentry permit. It's also called white passport by some and unlike AP does look like passport. The embassies usually would stamp their visa there, but still need to check with them first. The problem is NSC takes 12 months now to process reentry permit according to their processing times. It sure sucks.
The other thing I learned is about so-called 'world citizen passport' that can be obtained easily and used for travel. And even lot of countries recognized those passports, it's still appears kinda fishy, cause the acceptance is by 'de-facto" (case per case). I read one woman for her WC passport confiscated as illegal in South Africa. Anyone can shed more light on WC passports issue?
I'll post more info when I find