Can a DOI identify a web site?

Hello,

I have reading about DOIs and I just cannot figure out if a
web site counts
as an "object" or if pages within the site must
have separate DOIs.
Does the (usually changing) web site content make it
difficult to link to
content?

Can a web site have a DOI that relies solely on metadata so
that when the
site changes URL the DOI follows the site?

I am doing my degree in library and information studies and
I have seen web
documents linked by DOI but have not yet come across
DOI-linked web sites
when they are included in a library catalog.  It would be
useful to have
more stability in catalog web site links.

Thank-you for your time,

Christina Struik
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