Every closed immersion is a finite morphism. Can you give an example of quasi-projective varieties $X\subset Y$ such that inclusion $X\hookrightarrow Y$ is not finite? Same with Y projective?

Thanks!

Edit: Sorry this question is very simple, I made a mistake in reformulating asking the question. For a corrected version, check out this one.

Every closed immersion is a finite morphism. Therefore, restriction of a finite morphism to a closed subset is always a finite morphism itself. Can you give an example of quasi-projective varieties $X\subset Y$ , $Z$ and a finite morphism $f:Y\to Z$ such that restriction inclusion $f|_X$ X\hookrightarrow Y$ is not finite? Same with Y -- projective?

PS.

Thanks!

Edit: Sorry the original version of this question was hilariously stupidis very simple, I made a mistake in reformulating this one.

Every closed immersion is a finite morphism. Therefore, restriction of a finite morphism to a closed subset is always a finite morphism itself. Can you give an example of quasi-projective varieties $X\subset Y$, $Z$ and a finite morphism $f:Y\to Z$ such that inclusion restriction $X\hookrightarrow Y$ f|_X$ is not finite? Same with Y -- projective?

Thanks!

PS. Sorry the original version of this question was hilariously stupid.

Every closed immersion is a finite morphism. Can you give an example of quasi-projective varieties $X\subset Y$ such that inclusion $X\hookrightarrow Y$ is not finite? Same with Y projective?

Thanks!