My phone was cut off for unpaid bills.

Literal

Fee nonpayment [reason-で] phone [object-を] was-stopped.

滞納 (nonpayment/delinquency) is a formal term. で marks the reason or cause. 止められた is the adversative passive of 止める — something unpleasant was done to the speaker by an implied agent (the phone company). This adversative nuance is distinctive to Japanese passive constructions.