Dad started having mini-strokes about 3 years after Mom passed. He'd always been very sharp and except for having type 2 diabetes was in good health. We took turns checking in on him, I developed a continually updated medical status that was very helpful, but eventually we had to use daytime care that before the end turned into around the clock care. But he was able to stay at home except for hospitalizations and a couple of months in nursing homes to rehab. He was a farmer and staying home was vitally important to him. Fortunately we knew local women we could trust that worked cheap (the primary stayed upstairs which was mutually beneficial especially during blizzards).
Near us, the best independent living option is a converted high school that is cheap (subsidized, starting around $400/month) and a couple of blocks from a grocery and a small downtown. A local dial-a-ride service can take them to doctor appointments and elsewhere in the county.
After the passing of a spouse it's best to not make major decisions for several months. Take things slow and easy. Don't smother but be highly available. Listen to them and their needs. If parent/grandparent are in good health and mind, just help to fill the void. If they need to move or need more care, contact a social worker at a nearby not-for-profit nursing home for ideas. Every state/locality is different. I recently started volunteering for our county respite organization where we offer a break for caregivers and found an amazing number (hundreds) of resources that are available in our rural county.