Title remains vested in petitioners as before, possibly subject to typical deeds of trust or similar financing liens, etc. If the right exists, it exists whether or not a notice of noncompliance is recorded to give public notice of BHA's claim. In this case, for example, BHA filed suit to enforce this claimed right, something BHA could have done without recording a notice of noncompliance. As discussed above, the notice of noncompliance does not affect title to the property. Nor does it affect possession.
Petitioners retain possession as well as title.
Legally speaking, petitioners can freely transfer title and possession. The constraints petitioners are experiencing on transfer of title and possession are practical ones, not legal limitations. For example, property subject to a lis pendens remains freely transferable as a legal matter. The notice of noncompliance involved here has no legal effect on title or possession, or on transfers of title or possession. It is because few purchasers or lenders would likely be willing to assume this risk that transfer or encumbrance of the property might be impeded.