staying back and H4/dependent visa validity

I am currently on H1B and in US. last month I was offered job in an US based company. I accepted the offer and currently my visa transfer in process. I have a family here so visa/H4 transfer is being done for my dependents as well. Now in case I change my mind and dont join the company of which I accepted the offer then based on some blogs I understand I can still continue to work with my current employer as I have checked offer details and there I can see the clause of at-will termination from both sides however I am in doubt if visa of my dependents will still remain valid as well if I continue to stay in current company after H1/H4 transfer is approved? Please advise.