From the look of your floor, it looks like you need a new floor for hygiene purposes.
Asbestos is dangerous because the crystals are extremely long and sharp and penetrate the cells that normally clean dirt from the lungs. The asbestos that would be coming from the area shown would be in pieces not the fine particles that are inhaled and cause illness.
Asbestos is not a toxin or poison, it is the physical structure that is dangerous.
Inhaling fine particles is a problem. If you are forced to keep the floor, then any sealant that encapsulates the part that you are worried about will safeguard you.
When the Liberty Ships (Inexpensive cargo ships built during WWII) were built, the construction crews worked in areas that were being insulated with asbestos fiber.
The particles were so thick in in the air that some cases it looked like a dust storm.
The workers did not use masks and inhaled quantities of the fibers which caused the mesotheliomas and lung cancer years late.
There were enough cases of illness that attorneys put together a class action suit that stirred up tremendous hysteria. Of cause, it's dangerous to inhale the crystals.
Auto Brake mechanics were at risk because of inhalation of the asbestos in brake linings.
In general, if it isn't inhaled, it isn't likely to be dangerous.
So, as I said have the floor replaced or seal the areas which are friable.
Once sealed, it is harmless.