Not sure what you mean by "through slab repair". Must not be "well known".

hokie66: I think the OP is referring to 'through-thickness' (i.e. full-depth) slab repair, as opposed to partial-depth repair.

Alan CA: If the damaged area is both large (in area) AND more than 50% of slab depth, it if often then a candidate for full-depth repair - BUT this is also influenced by the technique of concrete removal.

For example, if concrete jack hammers are used and the slab is rather thin, then such a technique cannot tolerate more than about 50% of slab thickness removal without damaging the good remaining concrete.

However, is hydrodeomolition is the concrete removal technique, then you may be able to justify greater slab depth removal/repair before you consider full-depth removal and replacement.

If also depends on the type of slab: one-way, 2 way, post-tensioned (especially unbonded PT), and also temporary shoring, existing reinforcement, etc.

Also depends on the cause of the damage (water intrusion, freeze-thaw, chloride, ASR etc etc), and the expertise and experience of the contractors too.

To add to Ingenuity's good response, with thicker slabs I have encountered situations where the top 4" is removed for a top surface delamination and the bottom 3-4" is removed for a soffit delamination, leaving a thin unreinforced area. Not good (unless you are the Contractor getting paid to do the work), and a really expensive way to repair a reinforced concrete structure. Through slab repair for sure when soffit and top surface deterioration coincide.

Thank you very much for your answers.
Yes, here in Canada a full-depth slab repair is called through-slab.
The reason behind my question is that sometimes you sound the cracked slab with a hammer to hear something hollow or sense large vibration, yet the recommendation is a top surface repairs or soffit only!
Other cases involve a slab that is cracked across its depth, and still you see a recommendation of top or soffit repairs only! I'm not convinced that this should be the proper case!

Quote (Alan CA)

Other cases involve a slab that is cracked across its depth, and still you see a recommendation of top or soffit repairs only! I'm not convinced that this should be the proper case!

A “slab cracked across its depth” - do you mean a flexural crack only, because if so, and there is no resulting spall, epoxy injection is a common repair technique, assuming the crack is dormant.