Raising rent on elderly couple

[Alexander Zurn]

I am a few weeks away from becoming a first time home owner. 3 Unit in Rhode Island. The property contains a 2 unit building and a 1 unit standalone cottage. This will offer a unique opportunity to be a landlord/property manager in a separate building then my tenants. I am certain of the numbers, the zoning, the structure, etc. and have really done my homework (thanks to all of BP!). My question now concerns future tenants.

I was recently at the appraisal and I (unfortunately) was asked to stay on the street while the appraiser did his inspection. During this time one of the tenants in the unit with the highest rent (still below market) really tried scaring me out of buying by bringing up points that I have already factored in and thoughtfully considered. Needless to say, I played it off but still took note of everything he said and triple checked it. All is well! However, during this conversation I was lead to think that it may be wise to raise the rents on this unit first because in reality they may try to do this with future tenants I try to acquire (i.e. speak out against the property, etc.). The only and exact point of raising rent will be to get it up to market value so if the tenants I am speaking of can pay, great! But I have a feeling they cannot. The wife of the couple is very sickly. She has had a tough winter, I know because I have heard stories during inspection, etc. and I have seen the proof of 16 stitches on her head from falling due to high blood pressure. My question is this:

Say I close February 1st, give a 60 day notice of rent raise (more than required) to fair market value (a difference of $300-$400 in what they are paying now) and they decide to leave. What happens if the wife becomes ill during the moving process? Assume worst case scenario, am I legally liable for any illnesses incurred during the moving process? What if she becomes sick and bed ridden during the time they are supposed to move out? My worry of course is that I would that I am responsible because I would be "kicking them out" (Would I be though?) but this could be the non-landlord/business attitude of my speaking and something that I will have to get used to.