This round for government seats or for management? ?

Stray Round Is that round of counseling which generally happens after Mop-Up Round. It is generally conducted by state counseling authorities.

It is generally conducted by state colleges to fill up any stray vacancy which may arise after Mop-Up round of state counseling (if at all seats are left then stray counseling is done by college authorities)Hope you find it helpful

let me know in the comment box if you are having any further doubts.

thanks

Dear student, the process of counselling for the stray round is same as other rounds of counselling process of NEET UG 2019. You will have to do the choice filling, and then report to the concerned college for document verification and payment of fees. Stray vacancy round is done only if the seats are vacant after the mop up round.

DGHS will send list of candidates, 10 times the number of vacant seats, to colleges for Stray Vacancy Round. 

Please note that there will be no fresh registration for stray-vacancy round.

Final Stray Vacancy Round will be conducted by Deemed/ Central Universities
Visit this page for full info : https://medicine.careers360.com/articles/neet-counselling-faqs