I'm looking to share housing with an elderly person. Is this a plausible fair option?

Be certain you have a lease. Be sure you have a caregivers contract that spells out exactly what you will and will not be required to do.

there have been people who have come here in the past because the senior or the family decided the work was not enough to allow them to continue to stay and they were told to leave immediately. So. Be sure you have it all in writing and signed. Be sure to include the terms of termination too. You don’t want to be put on the street by the senior or her family.

I don’t see why not. But you must have a very clean background. Any Senior or their family worth working for should do an extensive background check before they hire you, up to and including a BCI report and fingerprinting. Make sure you have a signed Caregiver’s Agreement in place, preferably drawn up by an attorney. Bear in mind that unless you have another job that offers it, you will not have e health insurance or a retirement fund provided by your employer.

Have you considered Care.com or Indeed.com?