Single Ending:
Probably the most unsatisfactory ending ever, but it's Albel's default ending. We see Albel walking through a dungeon (that appears to be underneath the castle of Airyglyph), talking to himself about why the elite investigative team hasn't come back yet. Suddenly he hears a voice.
Then, a demon appears, who introduces himself as Romero, King of the Dead, created by the God of Death Folstar. He comments on Albel looking like a fighter, but he'd be no match for him. Romero adds Albel should go home, unless he prefers to become one of his mute servants. Albel answers with Romero being the cause of the problems. After the threats and cockiness, Romero says he'd never sully himself to fight a lowly mortal, and summons a couple of servants; Korima, Raxa, Mizva, Sazka. They appear to be the subordinates Albel was looking for.
Albel, being shocked, he draws his sword and prepares for battle. Romero replies with the following:

"You, who were abandoned by the gods you served, and left behind on this land...
May I, in my great kindness, extend a special hand of charity to you, and retrieve you as my own?"

Albel scolds his subordinates and says "Look at what happened to you, fools! Think of your place!"
Then the battle starts, though we never get to see their fate. Who wins and who losses and what happened afterwards is unknown.

Possibilities:
We don't get to see how the battle progresses, so we don't know who comes out as the winner, which is a pitty. I would've loved to see how the battle went but Tri-Ace left us hanging. Their fate is officially unknown and all we can do is guessing what could've happened.
Albel is quite a strong warrior, but his opponent is Romero, the King of death. And a demon to be precise! I don't like to say it, but there's quite a chance that Albel lost the battle, though how strong Albel is, he's still a mortal. He either died, or became a servant or slave.
As a back-up, I have the post-game dungeon the Urssa Temple. You'll fight the people not in your party (and they're having a sidekick), and when Albel's not in your party, you'll fight him. Interesting to say, Romero is his sidekick. But then again, the Fayt you'll fight later on is fake. But it's interesting nontheless and I wonder if there's any connection.
But there's allways the possibility that Albel wins of course, though realistic speaking, the chance is small unless some kind of miracle happened. But who knows how logic can twist. And, Albel has the Crimson Scourge after all, the sword said to be able to cleave the sky in two! In short, he either won or lost, and they didn't even left us a hint!

The Ending with Fayt:
You will see this ending when you complete the game with Albel in your party, and both Albel and Fayt need to have enough affection points to each other. If you want to know how that works, please look for an affection FAQ on gamefaqs.
Anyway, the scene will start with Albel and Fayt in the wilderness, being kinda lost. Fayt suggest to go camping, but Albel starts complaining about Fayt kicking him and waking him up in the middle of the night.
Fayt gets preachy, telling Albel that he screams in the middle of the night because of his nightmares, that he should look to his own fauls before finding faults in others, and that it was his fault they were wandering around in the first place. Albel got into a "brouhaha" with the lord of the last town, and apparantly they got kicked out before they could buy a map.
Albel replies with a random insult, and then they get surrounded by five enemies (apparantly send by the lord of the last town). Albel draws his sword, and Fayt tells him to go easy on him. Albel being Albel refuses of course XD
After the battle, Fayt complains about Albel being too hard on them. Albel replies with:

"Lessons cannot be taught by a gentle hand.
These types won't learn anything unless you lay them up for a week."

Possibilities:
Quite a funny ending if you ask me, I like them bickering. There are several possibilities; one being they'd be lost forever (which I doubt), other being eventually finding a town. There isn't really much for discussion here, I'll leave that open for fanfiction.