It is good to note that you are aiming to initiate good HR practices.
Your establishment/branch should be covered under (Name of the state) Shops and Commercial Establishments Act and as per this enactment also employer should issue appointment letter and thus observe good HR practices.
Standing Orders (cetified/model) may also be applicable to your establishment. There are many threads on it which you may find relevant e.g;
https://www.lawyersclubindia.com/experts/Standing-orders-442266.asp#.UtKr1dIW1MA
If you have deputed your employees at your client’s establishment they shall continue to be your employee and if the client has asked them to leave its establishment then they shall come back to you and you have to provide wages and tasks to them or they may succeed to claim retrenchment, lay off compensation.......................
Since client is not their employer your client can not terminate or relieve them from employment.
You or your client can not ask/demand/extract resignation.....................................it can be termed offence.
IN case the employee has absconded then first of all being HR personnel you may scratch and dig to find the basic reason ‘Why the employees’ resort to absconment?
In case the employee absconds the employer may issue communications then show cause notice by redg. post and even advt. in paper and later terminate as per process...................................and complete the process.
If the order of termination is bad the onus is on employer.