When someone dies who was receiving continuing health care from NHS?

What happens to their property? If it is left to relatives, do they then have to repay the NHS for the care or not?

The term 'continuing health care' is a specific type of funding. It recognises that, in other circumstances, the patient might very well be in a hospital or hospice, but that they have chosen to be cared for at home. Therefore there is no claim against their estate. They were entitled to the funding under the NHS.

No they do not have to repay the NHS.

The NHS was founded to provide free health care from the cradle to the grave.
If the relatives want to give something back to the NHS, then that's their choice.

NHS care is free at the point of servce, it's different for social care (but this is provided by the local authority not the NHS) which is means tested accorded to the so-called Fairer Charging regime. The charges would be discussed upfront though, with either the client or their representative. They can't retrospectively charge someone who has died. Contact you council's social services office if you are unsure, or look up 'fairer charging' or Fair Access to Care' on either www.dh.gov.uk or www.csci.org.uk.

As long as they were entitled to received free care under the NHS they wont be a bill.