I compare the aging process to a train in motion. The train starts moving the first day we are born. As we get older the train picks up speed and as we experience more medical problems the train increases speed. If we take action regarding the medical problems the train stays on the tracks and may slow down. As we get older the same thing happens with our ability to remain independent. If one refuses assistance, the train will eventually wreck. For many adult children they can see the train wreck coming, but don't how to stop it.
In the ideal world all members of a family live close to their parents and, with the approval of the parents, help with their parents needs. One member will do the lawn and snow removal; one will do the grocery shopping and doctor appointments, while the other will do the laundry and cleaning. The entire family works together to keep their parents' train on the tracks.
The ideal world seldom exists these days. Family members are spread throughout the world, dual income families working, and children's activities make it difficult to be there for parents. This coupled with siblings' inability to work together on the same agenda, and parents' refusing to admit their own aging issues makes the train move faster.
Approaching a parent about needing help can be very uncomfortable to say the least. This discussion is a family matter, not yours alone (unless you are an only child). One family member is assigned to assemble a list of concerns with input from all the siblings. Keep in mind that it is not uncommon for one family member to attempt to undermine the attempts of the other siblings for personal gain. Quite often this strategy is used when there is financial gain to be made or to position within the family.
Timing is everything when discussing sensitive matters such as these. Hold the discussion in a non-threatening private surrounding; generally the privacy of their home is best. At the meeting present the list of concerns and be a specific as possible by citing examples such as falling, bills not being paid, nutrition concerns, hygiene. Be prepared to offer alternatives. Either the family can step in and share the duties or an in-home service provider can be hired to provide the help required.
It is not uncommon for parents to refuse the help. Keep in mind that it is not IF the time will come, it is WHEN. It could be that the timing was not right, or the parents need time to process what is happening. Consider setting up another meeting in the near future to revisit the concerns.
If your parents refuse help and are not safe, there are legal alternatives to consider. Move very carefully in this area because this may be a point of no return regarding your relationship with your parents and possibly siblings. I suggest calling your local county aging office to understand your options.
In any case, do what's needed stop the train wreck from happening.