Firtly, please note that Google Answers does not provide legal advise,
etc.. See the disclaimers at the bottom of the page.
With that said, I'm going to make a few assumptions. 1) That your
parents are your legal parents -- and you can prove that with
documentation (i.e. they aren't just close family friends that you
call "parents"). 2) You are over 21 years old.
First issue: Your parents are "immediate relatives" and hence able to
have an immigrant number immediately available to them.
Secondly, the I-485a does not apply to them as they are immediate
relatives (i-485a is a $1000 penalty for being out-of-status while
filing an i-485 adjustment of status).
Therefore, in your parents case, being out-of-status will not incur a
penalty. However, strictly and technically speaking, your parents may
never be out of status, but, that issue is overlooked when it is an
immediate relative. However, if the application fails they may become
excluded from the US for a period of time. Also, they must NOT leave
the country until the i-485 is approved or an approved Advanced Parole
is filed. If they leave the country while out-of-status and with no AP
filed, they may be deemed to have abandoned their i-485 and, in
addition, be excluded from returning because 1) they overstayed their
visa AND 2) they are intending immigrants. You'd need to start over
again and file in their country of origin or through the district
office that would serve the country they are from.
Bottom line is this. If you want to be really good about everything
(and pay more money) file the i539. However, the odds are that you
really don't need to do it--but, make sure they don't leave!!
Please request clarification if any part of this answer is unclear
prior to rating and thus closing the question.
Oh, one other thing. The above is not legal advice. I am not
responsible if they kick your parents out of the country, etc.. (But,
I haven't had that happen yet, so, you're probably safe :) )
A quick read through of the forms on uscis.gov was done to refresh my
memory. But, I am quite proficient with family based immigration, so,
no real search was done.