As a consequence the exit visa situation would also have to be amended in light of there being no sponser.
Qatar could still keep an eye on people arriving in the country as work permits would stil have to be prearranged to obtain a visa. Anyone coming in on a tourist visa and trying to work will be dealt with as under the current system.
There will probably need to be a central registar where employees have to inform the government of their new employer; and employers will have to inform the register when someone leaves their employ.

having said all this I can't see any major changes actually happening soon, or if at all.