An application reads Unassigned when it isn't linked to any profile. That happens in two situations:

Either way, the application itself is completely unaffected. It was still sent, the employer still received it, replies still reach you, and everything in its inbox and timeline is intact. The tag is purely for your own organisation.

On the application, open the ⋯ menu and choose Move to profile, then pick the profile it belongs to.

You can do this with any application, not just unassigned ones. It's handy if you applied from the wrong profile by mistake.

There's no need to move everything. Tidy up the ones you care about tracking and leave the rest; an unassigned application works exactly like any other.

Your applications board has a Profile filter, so you can look at one profile's applications at a time instead of the whole pile.

This is where moving applications pays off: once everything is tagged, you can see how each job search is actually going on its own terms.

That's expected if you only have one professional profile. With a single profile there's nothing to tell apart, so Sprout hides the tags and the Profile filter entirely to keep things clean.

They appear as soon as you create a second profile:
👉 Using Multiple Professional Profiles (and Multiple Resumes)