Net Borrowing Position for an LP

...it is clear that if a user's portfolio has higher -ve fCash (obligation) than +ve fCash (claim on Cash), the user is in a net borrowing position. If the inequality is reversed, it would be a net lending position.

Context: Liquidity provider's portfolio

To illustrate an example, assume a liquidity provider providing 100,000 Cash in a pool consisting of 100,000 Cash and 100,000 fCash. The added liquidity will constitute 50% of the liquidity pool. Note that you would also have an additional 100,000 -ve fCash in your portfolio.

Your share of the pool represented by the liquidity tokens would consist of 100,000 Cash and 100,000 fCash unless a trade happens in the pool. Here 100,000 +ve fCash will offset the -ve fCash in your portfolio.

Now, a lender comes to the pool and adds 20,000 Cash. This trade would disturb the pool proportion to 220,000 Cash and 179,323 fCash. Now your share in the liquidity pool is different from earlier; your 50% share now consists of 110,000 Cash and 89,661 fCash. Note that your share has 100,000 -ve fCash in your portfolio which is no longer offset by your share of the liquidity pool.

The imbalance in +ve fCash and -ve fCash creates a net borrowing position for you (LP). Now if you exit at maturity (time to maturity = 0), you need to swap some of your Cash for fCash such that -ve fCash = +ve fCash. In your case, the difference between the +ve fCash and -ve fCash is 10,339 (+ve fCash < -ve fCash). Now, at maturity fCash price is 1 thus you would need to swap 10,339 Cash for 10,339 +ve fCash.

After swapping, you would end up with 99,661 Cash (110,000-10,339), 100,000 +ve fCash, 100,000 -ve fCash, and fees/incentives.