Police were called to Drews Holloway South at around 8.43pm on Tuesday, July 20, to reports of people arguing and fighting.
A 53-year-old man, from the local area, was taken to hospital with life-threatening head injuries.
On Thursday, a spokesman for West Midlands Police said he remained in a critical, but stable condition in hospital.
A 29-year-old man from Halesowen, who was arrested at the scene on suspicion of assault has since been released on police bail.
Parts of Drews Holloway South was cordoned off on Wednesday while police investigated the incident.
A spokesman from West Midlands Police said: "To help us understand what happened, we need your help. Please check your CCTV and doorbell cameras to see if they captured anything.
"We also want to hear from you if you saw people arguing or fighting. You can talk to us via our website’s live chat tool. You’ll find it at west-midlands.police.uk.
"We know that telling us things about neighbours is very hard, so you can stay 100 per cent anonymous by calling the charity Crimestoppers on 0800 555 111."
Alternatively, contact West Midlands Police on 101.