For the fiscal year 2004 I decided to enroll in a Flexible Spending
Account for 5400 dollars.  This money was used in mid January for
surgery. Each paycheck I continue to contribute to the flexible
spending account.  It's now march and I still have a number of
payments to complete the year.  For ease let's look at this as money
set aside, 5400, as of today money used, 5400, money I've contributed
to date 900, so I still owe my company 4500.   In about 2 weeks I will
be leaving my current company.
My question is - 
Since I am leaving my company do I still owe them the balance of my
flexible spending account?  Please include supporting websites or
documents.
I'm asking because I've heard that you don't have to pay your company the balance.

"I'm asking because I've heard that you don't have to pay your company
the balance."
I'm interested to know where you heard this. I don't believe a company
would give you a "gift" like that for leaving.  FSAs are subject to
strict IRS regulations and I am sure you would have to pay back the
difference between what you have contributed and what you have been
reimbursed.

I don't have enough reliable information to post an answer.  However,
the research that I have done seems to indicate that the question may
not have been finally answered by rule or statute but rather is in the
province of IRS staff interpretation.

But in light of the advice you got from research_help in a comment, I
should note that it appears that many employers require employees to
sign an agreement that any "negative balance" in a health FSA account
will be reimbursed from the final paycheck of the employee when he or
she separates from the company. Presumably, such an agreement is often
required by a company as a condition of granting severance pay, for
example.

However, some online (non-IRS) sources indicate that while the IRS
does require an employee to be able to run a negative balance in his
FSA in a given plan year if it would ordinarily be made up by
contributions during the rest of that year, the law and regulations
don't specifically require the employee to reimburse the company if he
leaves during the year.

The issue that I have not been able to nail down is whether the IRS
formally or informally currently blesses these reimbursement
agreements for departing employees.

markj-ga

As markj-ga noted, some employers may require employees to sign some
sort of an agreement to pay back any negative balance; however, a lot
of companies don't, from my experience and from a quick search of
Flexible Spending Account plan rules online.  For example, at the
company where I work, we've had this situation before and had to "eat"
the negative balance of terminated employees.
IRS regulations do not require employees to reimburse the negative
balance on termination; they do require the plan to allow employees
access to their full potentially contributed balance at the beginning
of the year, know as "uniform coverage rule".
So I would suggest you check with your FSA plan administrator -
request a copy of your plan rules, and read them very carefully.