Many companies do not issue appointment letter (which is often illegal) but that does not take away the right of an employee. Possession of ID card is enough to prove your employment. Apart from visiting card try to get any other documents like any letter of authority issued to you or any internal memo given to you etc. for safety. Hope the company has attendance register as well as salary register which can be beneficial to you too. How was your salary paid?
There are two aspect here:
First salary. Generally company has to pay salary within 7-10th of each month. If there is a delay, you can demand in writing from the management and further can make official complaint before the competent authority.
Secondly on the point of termination, if you do not tender resignation, you will remain employee of the company and will be entitled to get salary until the company terminates you. Wait for the right moment for the company do any mistake.
18th January 2017 From India, Kolkata