If a person was initially capable of performing all the rites of Hajj and was hired to perform Hajj on behalf…

If a person was initially capable of performing all the rites of Hajj and was hired to perform Hajj on behalf of someone else, but during the rituals he became incapable—due to illness, for example, or a broken leg—and thus was unable to personally perform ṭawāf (circumambulation), sa‘y (ritual walking), and the like, is it permissible for the proxy to delegate someone else, and would that be sufficient?