This sounds so cartoonishly evil that it's difficult to believe, but people have actually been deliberately injected with human cancer cells and they generally do NOT get established.

Horrible but true:

Tuskegee syphilis study not America's only medical scandal https://aquila.usm.edu/cgi/viewcontent.cgi?article=1242&context=ojhe

In general it's going to be ok because a healthy immune system is going to recognize the cells as foreign. The problem with getting cancer for the most part is that they ARE your cells. (Ideally your body recognizes your own cancer cells anyway but you get the idea.) If you're immunosuppressed for whatever reason it's possible.