Modern slavery type smuggling, as with the Vietnamese who died at Purfleet, will follow the debt model but those people will go into whatever has been arranged for them. It might be nail bars, cannabis farming or prostitution. Straight into the black economy; no need to claim Asylum.
Practically all of those on small boats claim asylum. They are then subject to a system that will decide whether they have a justified claim to protection from harm or not. If that system were made to work, including a fair and independent appeals process, there'd be less controversy about asylum accommodation.