One of the features of SharePoint is the ability for users that need access to a site, and are denied access, through the Request Access process.

To enable or review these settings

• Go to Settings | Site Settings | User and Permissions and click on Access Request Settings. In the Access Request Settings dialog box, select the check box next to Allow access requests. Then provide an email address of the individual you would like to manage this feature.
• If a site has multiple groups with the same permission levels (Owners, Members and Viewers) but there is not an assigned default group, then you will see the problem where access requests will either not display for the impacted user or an owner will not be able to approve requests.

Windows PowerShell script to change each of the groups for a site so that each is identified as the default group for Members, Owners and Visitors. You will need to a the Microsoft.SharePoint.PowerShell add-in at the top of the script to get the SharePoint references.

#Members Group
$web = Get-SPWeb "https://sharepoint.contoso.com"
$groupToMakeDefaultMembersGroup = $web.Groups | ? { $_.Name -eq "Team Site Members" }
$web.AssociatedMemberGroup = $groupToMakeDefaultMembersGroup
$web.Update()

#Owners Group
$web = Get-SPWeb "https://sharepoint.contoso.com"
$groupToMakeDefaultOwnersGroup = $web.Groups | ? { $_.Name -eq "Team Site Owners" }
$web.AssociatedOwnerGroup = $groupToMakeDefaultOwnersGroup
$web.Update()

#Visitors Group
$web = Get-SPWeb "https://sharepoint.contoso.com"
$groupToMakeDefaultVisitorsGroup = $web.Groups | ? { $_.Name -eq "Team Site Visitors" }
$web.AssociatedVisitorGroup = $groupToMakeDefaultMembersGroup
$web.Update()

If you turn off the feature, you can re-enable the feature by adding an email address to the RequestAccessEmail property. Hope this helps solving the problem around assigning default groups and enabling the Request Access feature in SharePoint 2013.

#Enable Access Requests after it was disabled
$web.RequestAccessEmail = "user@mydomain.com"
$web.Update()