I bought a HDB flat with my parents and paying for it MYSELF, still left 15 years. They are occupiers only. If they get another flat due to inheritance, can they move there while I continue paying?

From what you describe, you're the owner and your parents are occupiers, so this comes down to HDB's occupier rules, and HDB decides.
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HDB's page says you can remove occupiers who no longer live in the flat only if it doesn't affect your own eligibility to keep the flat. The example it gives: taking the occupiers out could mean you no longer meet the family criteria of the scheme you bought under.
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So I'd ask HDB that first, before anyone moves out, and ask at the same time how inheriting another flat would affect your parents. The page is here.

It depends on ownership and regardless of who is paying for the HDB. Generally, you can only own one HDB in your name.

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