This work considers the problem of integrated sensing and communication (ISAC) with a massive number of unsourced and uncoordinated users. In the proposed model, known as the unsourced ISAC system (UNISAC), all active communication and sensing users share a short frame to transmit their signals, without requiring scheduling with the base station (BS). Hence, the signal received from each user is affected by significant interference from numerous interfering users, making it challenging to extract the transmitted signals. UNISAC aims to decode the transmitted message sequences from communication users while simultaneously detect active sensing users, regardless of the identity of the decoded and detected users. In this paper, we derive an achievable performance limit for UNISAC and demonstrate its superiority over conventional approaches such as ALOHA, time-division multiple access, treating interference as noise, and multiple signal classification. Through numerical simulations, we validate the UNISAC's effectiveness in detecting and decoding a large number of users.