Yes, if the installment plan you negotiated is not backed by the proper legal documentation, the IRS can continue to levy and lien your property and assets. It is important that any agreement you enter into with the IRS is signed both by the company and by an IRS official.
Any agreement should be signed by the IRS because, simply put, the people who contact you collecting a debt from the IRS are debt collectors. They will say anything to get a payment from you and will typically record very little of the conversation for future reference. In order to avoid continual debt collection by the IRS, you need a legally binding agreement. The only way the agreement becomes legally binding is if it is in writing and signed by the IRS. This forces the IRS to be held accountable for the agreement.
If you are negotiating an installment plan with the IRS, do not make a single payment until the signed agreement is in your possession. This will ensure that the IRS does not take further action against your property and, if they do, they will be held liable.
However, if you have reached a point in your negotiations with the IRS that requires a written contact, it is always wise to seek the assistance of a tax attorney. By using an attorney for the contract, you ensure that the contract is airtight. In addition, if the IRS breaks the contract, you will already have an attorney on hand for challenging their actions. Remember that the only priority of the IRS is to obtain income for the federal government. This means that they will use any measures necessary to obtain funds from non-paying citizens. An attorney will ensure that the government does not take advantage of your rights.