My elderly aunt has kept her flat and moved in to live with her child(ren) and rented out her own flat for years. I think it's a good option as there's rental income.
I wanted to get a property with my mum and both of us will have to dispose of our HDB flat. My sister's take is that if my mum dispose of her current flat, she can never get an 'affordable' aka cheap HDB again. Apart from that, my mum's flat location is in a really good area/location. Though I want a new flat, I agree with my sister. This is to safeguard your parent(s). It's like a security blanket for them. Relationships are always fragile no matter what. Anything can change.