I have a client who is awaiting a decision on asylum application, and is currently able to claim HB and IS. If her stay is refused can HB and DWP recover the monies paid to her?

No, they would not recover.

The "transitional protection" given to those asylum seekers who were either entitled to benefit on 4 February 1996, or who applied for asylum on or before 2 April 2000, means that they are quite properly entitled while awaiting a decision on their asylum claim.

Transitional protection ends when a decision is made on their asylum claim.

These transitional protection rules are summarised on pages 240 to 243 of the current CPAG Handbook.

However, also useful is rightsnet's Asylum Seekers and Benefits Q&A