This work considers the problem of integrated sensing and communications (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 simultaneously 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 detecting active sensing users and estimating their angles of arrival, regardless of the identity of the senders. In this paper, we derive an approximate achievable result 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 effectiveness of UNISAC's sensing and communication capabilities for a large number of users.