If you apply for a position and an OFFER is made to you, you have 24 hrs. to accept or decline the position. If you accept you obviously won't get severance because you now have a new job. If you decline before the 24 hrs. is up, you are still eligible for severance. If you don't want the role you were offered but don't officially decline it within that 24 hr. period THEN you become ineligible for severance.
Reposted from @Ow4PZiR-dsz for first-hand info.