Depends on what kind of map & other systems you got going on.
I can only think of one time you can specify reactions to Blight in the Object Editor; HP Regeneration (nicely enough). So you can set the unit's HP regen to, say, -1/sec (or however much you want them damaged per second), and then set their HP Regen to "only while on Blight". Then you can just give them a passive, hidden/item-based ability for a normal Regeneration.
Unless, of course, you need them to have normal Regeneration only during the Day/Night/whatever, or something else stops you from using this.
In which case, the only other thing I can think of would be to spawn a dummy unit along with the Blight (in the epicenter) which has a modded Permanent Immolation, constantly dealing however-much Damage-per-Second to enemies around it. (perhaps the Dummy Caster can be like the Undead Buildings, have "Create Blight" itself so that you need only place the right Dummy to get a certain amount of Blight. Otherwise I'm not sure how you'll keep track of the Dummy... (then again, you needn't keep track of him if he's set to die automatically... But you'll have to do so...
using the very Blight he's spawned on. In order to do
that, you can have it so he has an insane HP "de"regeneration ability (killing him quickly), and then an equally-insane HP Regeneration set in the Object Editor, but "only while on Blight"; that way the instant the Blight around him is dispelled, he dies too (the Blight being the only thing regenerating him fast enough to stay alive. Crazy, but it just might work))
Hahahaha. Let me know if that helped at all, or just confused the issue.