Can your Landlord make you leave? If you fail to pay rent, he can serve a 3-day notice and begin eviction proceedings. The law does not recognize illness or leave of absence as a defense to unpaid rent.
Can your Landlord make you leave and then pay rent? If your state does not have a liquidated damages statute or a statute which mitigates damages in some fashion, then you are responsible for the rent until the end of the contract. Most states have a mitigation factor built into the laws, such as if the LL rents to a new Tenant within two days of your leaving, then you only have to pay for an extra two days after you turn over the key. Also, some states have a liquidated damages factor, which states that if it is in your lease and you and the LL sign, then you are responsible for a set amount of money if you breach your lease and move out by turning over the key.
Read your lease with an eye to language that limits the money you owe if you terminate the lease early.
As to the agreement the LL is asking you to sign, you probably should take a copy of the lease you already have (if there is one) and a copy of the agreement the LL wants you to sign to a local attorney. No one can make you sign anything. Get an opinion from a lawyer before signing.
Unless you waived your right to receive the statutory notice to vacate the premises, your landlord has to give you notice to vacate at least 10 in advance of bringing an eviction action before a magisterial district justice. If he fails to give you that 10-day notice by either hand-delivering it or posting it on your door, you can have the action dismissed. If he sends you notice by certified mail, that doesn't count and you can have the action dismissed. Assuming your landlord does everything right, he can only get a judgment for rent due and owing as of the hearing date, not future rents. (In Pennsylvania, a residential landlord has a duty to mitigate damages, which means he must try to relet the apartment promptly to lessen his loss.)
I agree with the other attorney, that your medical and financial problems are not recognizable defenses to eviction based on nonpayment of rent.