Do background verification companies also contact deputed (payroll) company HR during verification?

Hi There, I was working on let say X company payroll. After 2 years, joining the company, I was deputed to Let say Y company.
Now, I have left X company as things were not going well with Y company.
I got a proper relieving letter and experience letter from X company.
My question is, do background verification companies also contact deputed company HR during verification?
Moreover, after putting my resignation, I told my X company that I won't work for Y company anymore, if there is any work I would be happy to do.

Dear Friend, Background verification can be done from the company you were deputed. It can be done from both companies.
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Hi Akhil
Thanks for the answer.
My tenure with X company is "2 Years 9 months" and I was deputed with Y company for only "5 months".
Still do you think, future company may contact to Y company for verification.
What is the standard industry procedure to verify Deputation information.

Dear Friend,
To do background verification or not, if it is done then with whom, this is all the prerogative of your employer.
The employer can do your background verification from your neighbour also.