Laws vary from state to state, but requiring an excessive escrow balance is not legal. Many states have a cushion of 1-2 months which equals one or two months of escrow payments.
Fleet Bank got into a lot of trouble a number of years ago for requiring 6 months escrow or more and had to refund millions of dollars. That said, if $2000 equals one or two months of escrow, then the lender is within its rights to require that amount.
If you had a severe escrow shortage and the lender advanced funds to pay taxes and/or insurance, then they have a right to recover those funds. The length of time allowed to recover those funds may vary. By law, you should receive an annual statement which analyzes your escrow account to make sure the right amount is being escrowed. If you believe that amount exceeds state requirements, you should check with your state’s requirements via the banking department.
As an aside, a $2000 minimum balance would translate into $24,000 annual taxes and insurance if only one month was needed as a cushion and $12,000 if two months were required.
Escrowing is part of the Real Estate Settlement Procedures Act of 1974 (RESPA), enforced by the U.S. Department of Housing and Urban Development. Mortgage Companies must manage their escrow accounts in compliance with this federal law. Also back in 1990, congress passed a housing bill that requires lenders to issue itemized statements of escrow accounts to borrowers on an annual basis. Many lenders were already providing homeowners with regular statements of their escrow accounts but abuses were common. As mentioned in a previous answer if you had a serious delinquency this could simply be catching you up. I see this very common with new home construction where the property taxes we assessed on bare land and later the improved lot assessment was 10 times more causing a large shortage in a very short time after closing. The administration of escrow accounts is heavily regulated now and watched and it’s unlikely if your dealing with a large national lender there is an abuse but stranger things have happened. Contact the original lender you closed with to review you account and make sure everything is in order.