I don't think it's a question of being her family's property, it's just that dying is a very private and difficult thing to do. When my husband was dying, there was a week in which a few close friends were able to visit, but I felt it was more for their sakes than his, it can be quite difficult if you are very compromised appearing for others, and then there were the last couple of weeks in which he absolutely didn't want anyone except very close family, and the last week he was in and out of a coma. My friend was in 6 weeks and it was very close family only at that stage.
The difficulty is the OP doesn't have contact with a close family member or friend, which is why dropping a note with your telephone number in is a really helpful thing to do for the family as they won't know about you otherwise. Or just send one to the person and they can read it out.
It is also the case that when young popular people die, having been ill for years, they have a huge amount of friends, supporters and family who all want to be involved, but not everyone can see them without it overwhelming the person involved- and ultimately, if you were incontinent, unable to walk, unable to eat or in the last stages of dying, would you want to appear in front of people, sometimes there are other things going on as well (agitation, hallucinations), all kinds, depending how the cancer has spread, especially if it spreads to the brain, so there are good reasons why even close friends may not be able to visit up til the last.
It does not mean you did not matter to that person, nor that your relationship wasn't really special. It does mean it's coming gracefully to an end though and that's really sad. I just wanted to explain why people may limit access even to good friends towards the very end (and others may not, which is why contact details on a card is the best way forward).