The vaccines are not 100% protective. Some of the Covid vaccines are the most effective vaccines ever produced but it seems that about 5-30% are not as well protected as we would like depending on the specific vaccine used. And without more tests, no one knows if they are part of the 5-30% who are not as well protected. These vaccines do seem to be more effective at protecting against hospitalization and death. I don't have numbers on the top of my head (and I don't think we have good numbers yet) but there is still a more than an insignificant chance that a vaccinated person will die of Covid.
So if a person with Covid, vaccinated or unvaccinated, interacts with a vaccinated person, there is a reasonable chance that the vaccinated person will get covid too. I've seen numbers that put this at about 10% of the chance that an unvaccinated person would get Covid in the same circumstance.
There are people that for good health reasons, generally allergy-related, should not get vaccines. These people are vulnerable. The whole reason to try to reach herd immunity is to protect these and others who won't get vaccinated. I would expect that anyone who knows that they are not protected should take extra steps to protect themselves but what would really protect them the most is if there was less Covid floating around in the community.
A basic fact of virology is that the less of a virus that is floating around, the fewer chances there are that it will mutate. The more mutations, the more chance that a variant will arise that current vaccines will not protect against and we are back at square one. This is a worldwide issue so in theory giving a vaccine that one person refuses to take to another person in another part of the world is just as effective against mutations. From a practical perspective, a lot of vaccines in the US are being thrown out because they expire unused. They are not being shipped elsewhere.
One of the main things that public health officials worry about with a pandemic is overflowing the healthcare system. People with unrelated illnesses are dying because there are no emergency services available because they are being used up by Covid patients. So unvaccinated people who get seriously ill from Covid are putting the whole community at risk by using up resources that would not have been used if they had been vaccinated.
So I think that the best reason why an unvaccinated person might consider getting vaccinated is to help protect those around them, vaccinated or unvaccinated. Personally, that was my first reason for getting vaccinated when the opportunity came up. I wanted to help protect my community. Even though I am older and have some health risks, I still felt that the very minimal risk I was taking was worth the reduced risks associated with Covid to me, my extended family and the overall community.
If it were just a matter of only the unvaccinated get seriously sick and dying from Covid, I'd still implore them to get the vaccine for their own sake but it goes way beyond that.