Working permit change

I applied to work as an English teacher in Dongguan and they have sent me my working permit to apply for my visa. However, I then found out that the company sometimes do not pay their employees, and other bad reviews.

I have found a different job in Shenzhen and they have sent me a contract to sign, however I am worried they will not be able to apply for my working permit due to me having a working permit with another company.
The first company are telling me I will have will have problems going to China if I don't go to work for them.
Are they telling the truth? will I be able to work for the second company?