Depends on the circumstances.
For example, if there is a family emergency/death in the family/similar catastrophe, something time-limited, then sure, make an exception. Even better if the tenant contacts you with “I am going to be late on rent this month because of X, Y, Z. I will pay the rent by X date”. A good, responsible tenant (like myself) will let you know what’s going on and when you’ll get the rent.
If, however, it is not a time limited emergency then you may have to tell the tenant to go elsewhere, but it’s your option how aggressive you want to be with that. Which may also depend on your finances.
My former landlord had a tenant who was desperately ill, first on the transplant list for new lungs then off the list because she was too sick to survive the surgery, then finally in a nursing home. The last two years she was his tenant the rental income was spotty but he cut her a lot of slack because, obviously, she couldn’t work, disability pays crap, and she had been a reliable tenant of his family for decades. Basically, he accepted whatever money she could send him the last two years she was a tenant, and worked with her family to get her moved in the end and clear out the house. But that was an exceptional circumstance AND he had enough other tenants reliably paying to pull it off.
More commonly he’d start eviction proceedings in line with those already mentioned, because most people aren’t that sort of stable, long-term tenant.
Also - be careful of tenants offering to work in lieu of rent. I have done this in the past a few times, the best way to handle that is to pay the person for the work they do for you, rather than try to apply labor to rent. For example, during a period of minimal employment I cut the lawns and worked on the landscaping for several of the landlord’s other properties, for which I was paid an agreed upon wage. Then at the first of the month I paid the full rent. So yes, effectively I was paying part of my rent by working for the landlord, but that way the bookkeeping was a lot less messy and less prone to misunderstanding. Be sure that the tenant is capable and knowledgeable enough to do the proposed work.