Sorry of the delay in my response. This has been a hectic month for me requiring two trips back to the States. I am just now catching my breath.
There is no automatic transitioning of a student visa to a work visa.
Let’s assume your residency permit, based on the X-visa, expires in September and your program ends in August. You would then have a month or so to live legally in China while looking for work.
Once your residency permit expires, if you don’t have a job by then, you will have to downgrade your X-visa to a tourist (L-) visa. That would then give you up to three more months to look for work.
The only caveat is that once you downgrade to a tourist visa, depending on your province and the social connections of your employer, you may have to return to India to reenter China on a work visa.
Best of luck.