All self-managed arrangements come together in the morning. You have a worker who is ill, on holiday or who's got a new job and the support you had on Friday is not there on Monday.
If one person is all you have then that morning is a crisis. It doesn't need to be.
A second worker that is familiar with you. An occasional change in routine once a fortnight makes somebody else know what you do and can pick up more on short notice. This is the best backup you can get and why people forgo it because it appears to be an unnecessary expense.
A shortlist to keep warm. Two to three people who matched your original search who you have met once, and who you have verified the availability of every few months. A name is not a person whom you have met.
A page about you. What to do, how, what is important, what to stay away from, and who to call. Once written, given to anyone who steps in. It is a necessity, otherwise you will have to tell everything on the first day you meet a new person.
Others prefer not to risk losing a shift than dealing with a stranger in the home. That's a fair point and it's a plan, if it is a choice or an option not a default.
If you are that person, the answer is the second worker (not the shortlist), because you're safeguarding familiarity.
At the beginning and not in the first crisis. If you have to shortlist for a new arrangement, then shortlist for two jobs instead of one. It requires one additional meeting.
Consider what would happen if your primary worker doesn't show up tomorrow. If not, it's your challenge for this month.
Find Your Support Team. It's easy to find a second worker as the search is quick to repeat.