Is it permissible to continue working for someone who does not fulfill his promises, and what is the ruling on leaving this job if no other work is available, and is that considered a disruption of one's livelihood?

It is advisable to consult with relatives, friends, and people of knowledge, perform Salatul-Istikhara (prayer for guidance), and recite the Istikhara supplication mentioned in Sahih Al-Bukhari. It is also possible to search for another job, and increase seeking forgiveness (Istighfar) as it relieves worries and brings provision. Furthermore, there is a supplication narrated from the Prophet, peace and blessings be upon him, in Sunan Abi Dawud, seeking Allah's help from worry, sorrow, helplessness, laziness, cowardice, stinginess, being overwhelmed by debt, and subjugation by men. It should be known that provision is guaranteed by Allah, and reliance upon Him does not negate taking necessary measures.