The Third Circuit has determined that a non-citizen who enters the US through the visa waiver program (VWP), receives asylum, and re-enters the country as an asylee at a later date, is no longer subject to the waiver of rights that attaches to a VWP entry. Thus, if the asylee is later convicted of an aggravated felony, the Department of Homeland Security must place him in removal proceedings, not re-open the asylum-only proceedings through which he was originally granted asylum, in order to terminate his asylum status and seeks his removal. In these removal proceedings, the asylee can apply for adjustment of status.
The full text of Kosh Ishmael v. Attorney General can be found here: