Usually, the tipping point comes when something goes wrong. Someone has a fall, or is ill. And family aren’t able to help as much as they would like to (either they live away, or have their own commitments and are frantically busy themselves).

At this point, families often arrange for an hourly visiting carer to come in once a day to check everything is OK. This brings reassurance that their loved one is fine, the person with the carer starts to get used to the idea of care and if anything else goes wrong, such as a sudden illness, eyesight deteriorates further, etc), the carer can just come for a little bit longer.

As time goes on, often our client finds things increasingly difficult and needs more help. It might be they need help washing, or dressing and undressing. In this case, the carer just comes in more often. Throughout, the carer is encouraging their client to do as much as possible themselves, so they stay as independent as possible, for as long as possible.
If the person needing care then maybe has an operation, a live-in carer can come in and be there full-time for the whole convalescence period. Once they recover, we can easily return to their old schedule of an hourly visiting carer.

As someone becomes more frail, and needs someone there all the time, a carer can come to live-in. The carer is there to help their client to stay as independent as possible, and give reassurance that there is someone there for support, always.
This way, all the time someone has needed help and care, they have been at home and encouraged to remain independent, busy and part of their group of friends, family, community. They have stayed useful and wanted, key factors in preventing loneliness and poor mental health.