You don't "see it now". Allowed Claims do not have to be paid in total in order to be Satisfied in Full.
Allowed Claims are legitimate claims, but this is a BANKRUPTCY.
Example: You owe $10,000 on a credit card. You claim bankruptcy. The credit card company has an Allowed Claim against you for $10,000. They might get nothing. But they can negotiate with you to receive something, let's say they agree to accept $1,500. When you pay them the $1,500, they are Satisfied in Full and they go away.