Who pays
An assessment approved before closing is usually negotiated in the contract: the seller pays it, credits you, or you take it on at a lower price. One voted after you close is normally yours. Get the resale certificate or estoppel letter, which lists approved assessments, and read the last year of board minutes for anything being discussed.
What to check
The reserve study and how much is actually saved. Upcoming repairs in inspection reports. Fee increases and insurance costs. Lawsuits. Whether lenders are still lending in the building.
Use the time you have
Most contracts give you a short window to review association documents and back out or renegotiate. Ask for the documents the day your offer is accepted.
General information, not legal advice. Rules vary by state and by your governing documents.