What happens if a unit recruited with "Bonds of Loyalty" dies due to paralyze?
You can use Bonds of Loyalty to recruit another unit with the bonus it offers.
There is a discussion about this question on BGG. The last poster quotes Paul Grogan, who is the maintainer of the Official FAQ for the game and appears to be at least partially responsible for the writing of the rule book. A unit recruited by Bonds of Loyalty cannot be disbanded, but Paralyze destroys the unit and removes it from the game. This is probably the &quot;clever way&quot; that Paul Grogan was talking about of replacing a Bond of Loyalty recruited unit.
From Paul Grogan's post regarding Bonds of Loyalty, emphasis mine.

The other skill is Bonds of Loyalty. ...
First of all, this skill gives you an extra command token. i.e The Skill itself counts as another command token, so you can recruit one more Unit. When you gain this Skill, you add 2 more regular Units to the Unit offer.
The Unit that you recruit into this slot costs you 5 less Influence to recruit. But it doesn't stop there. This unit is so loyal to you, it can be used even in situations when you couldn't normally use Units (i.e when down Dungeons or burning down a Monastery)
The only slight downside of this Skill is that you cant dismiss voluntarily the Unit that you recruit into this slot, so if you use it in the early game to recruit a low level Unit, you're going to have to find a clever way of getting rid of it if you want to replace it.

Paralysis definition from the Rulebook.

If a Unit is assigned damage by a Paralyzing enemy and would be given a Wound, it is immediately destroyed (remove it from the game)