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It needs to be stripped with an appropriate VCT stripper (chemical), then it needs to have 3-5 coats of a metal-crosslinked acrylic floor finish applied. This process would need to be repeated based on traffic and your expectations of what you want the floor to look like. This can be done with a mop and bucket, but the results are generally much better with the appropriate equipment.
VCT is essentially a solid product with no built-in wear surface. That's why it's one of the cheapest floors you can (could) buy. The trade-off is that the cost of ownership (maintenance products & labor) is much higher than today's flooring options.
There is another alternative, but it's considerably more expensive and it would require hiring someone to do it. You can apply a semi-permanent coating to a VCT floor. These are specialized urethane topcoats made for this purpose (not just any old urethane) and it needs to be done by someone who has the equipment and experience to do it correctly because it can get messed up in a hurry. Typically, the companies who do this type of maintenance are commercially oriented and it may prove difficult finding someone to do such a small application in a basement. Probably much easier in the long run to go with the first option.
However, the upside is, if done correctly, you may never have to strip and re-apply finish to the floor again.
You can purchase a test "kit" from your local Lowe's or Home Depot to have the tile tested for asbestos. It's possible, if the flooring is truly that old, that both the flooring and the underlying adhesive may contain asbestos. However, that doesn't mean that in its present state it's going to harm you or your family. The asbestos fibers are encapsulated into the flooring and the adhesive and unless they are disturbed by removing the tile then it won't harm you. The loose fibers have to be breathed in to cause harm.
A word of caution...BEFORE you do anything to disturb or remove the floor, make sure that you are familiar with the requirements for doing so. Municipalities, Counties, & States can all have guidelines that dictate what you can and can't do as a homeowner to safely remove the product. Your local building department should be able to alert you to any requirements you must comply with for removal and disposal. If you find that there are none, then a good reference on what to do would be found here:
https://rfci.com/wp-content/uploads/2018/04/RWP_MASTER_English_2018.pdf
These guidelines were developed in conjunction with OSHA and can serve as a practical guide where no other ordinances, codes, or laws for abatement exist.
I would strongly caution against removal of this flooring and the adhesive. Given the age of the home, it's safe to assume that there is no intact vapor retarder underneath the basement slab and right now this floor is very likely serving as a pseudo vapor retarder. If you remove this flooring and adhesive in order to put in a new floor, you could very likely be opening up another issue and creating a slab moisture problem.
Wish you the best and please let us know if you have any other questions.