What uually happens is that the contractors totally seal everything in ie they make a tent around what needs to be removed. The tent contains any loose fibres (although they usually damp things down with a special solution to try & minimise airborne fibres). The tent should ensure that no asbestos 'escapes'. Air tests after everything has been taken down should double check that they are no airborne fibres.
Personally - I would remove what I could from surfaces & possibly seal cupboard doors with tape.
If you are worried - get them to do lots of air samples from around surfaces (get them to wipe over the surafces & then take measurement)