Which insurance companies provide Short Term Health
Insurance in New York State for people that have been laid off of
their job?, if there are not any, what is the reason?

I don't know about New York in particular, but all states are required
to participate in the HIPAA program (Health Insurance Portability and
Accountability Act).  This is the one remaining portion of the
Clinton's health plan.  It is most useful for people who would be
uninsurable because of some pre-existing condition who have had group
coverage by their employer, which is terminated for any reason.  The
way it works is that after exhausting the 18 months of COBRA coverage
(you pay the premium your employer would have paid for you if you were
working), you can apply to get guaranteed coverage under the HIPAA
program.  The details here depend on the state you are in, but in
California, any health insurer that offers individual policies in CA
must offer at least one HIPAA plan.  There, unfortunately, is no
requirement for the coverage plan offered or the price they can
charge.  So some insurers that do NOT want to participate greatly
limit the coverage and charge an arm and a leg.  However in CA, both
Blue Cross and Blue Shield offer reasonable plans at reasonable
prices.  The prices are higher than their rate for ordinary (well
person) health insurance, but you are guaranteed to be covered with no
pre-existing condition restrictions.  This has been great for my
family and me since we have had various preexisting conditions.  IT IS
ESSENTIAL THAT YOU ACCEPT AND EXHAUST THE COBRA COVERAGE TO GET INTO
THE HIPAA PROGRAM.  Make sure you do that!  If you get another job in
18 months, all you will need is COBRA, but if it lasts longer, you can
get HIPAA.

http://workingtoday.org/
Here is an excellent source for insurance in New York City.