I think that they meant to write "assignee" in the source text. Here are some entries for assignee in En-Sv affärsekonomisk lexikon:

1
Övertagare
Förvärvare
Successor

2
Fullmäktig
Befullmäktigad

3
God man (i konkurs m.m.)

Hopefully this will help yourself or another native Swedish speaker to choose the right word

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Note added at 1 hr (2011-10-08 16:05:01 GMT)
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I see. Well you are correct that it is not a misspelling.

It seems like assign as a noun is still a synonym for assignee though. The description you gave in your discussion entry sounds just like what assignee means.

This dictionary defines it as a synonym as well:

"noun
9.
Usually, assigns. Law . a person to whom the property or interest of another is or may be transferred; assignee: my heirs and assigns." - http://dictionary.reference.com/browse/assign

I think you may still be able to use a Swedish translation for assignee. The example in the dictionary that read "my heirs and assigns" makes me suspect that "assigns" as a noun is primarily used together with heirs as a fixed expression.

Perhaps in other parts of the document where it is not used with heirs it may be written as assignee instead.

Anyway, I guess this is all somewhat meaningless: you already know what it means based on your discussion entry and now you just need to choose the right Swedish word. It sounds like some kind of successor or efterträdare to me.

By the way, I just also found an entry for "assigns (noun)" in En-Sv affärsekonomisk lexikon:

successorer
efterträdare
övertagare
arvingar