I had the same issue today on a site with Kerberos authentication. It started after I extended the web app using Powershell. I was seeingsaw the same errors in ULS logs as you have mentioned. For some reason the authentication mode for this web app changed from Kerberos to NTLM and the web app got converted to Classic mode. I switchedconverted it back to KerberosClaims mode and enabled kerberos and its back up. The ULS error 'Neither a claims user nor a claims user suffix' suggested something was wrong with claims mode. Checked it by running this command and the site loaded fineoutput was false:
$WebAppName = "http://"
$wa = get-SPWebApplication $WebAppName
$wa.
UseClaimsAuthentication
Another strange thing is the authentication providers page for this web app has changedfalse
Converted back to SP2010 style, I'm on SP2016.claims mode using this command:
Convert-SPWebApplication -Identity yourWebAppUrl -To Claims -RetainPermissions [ -Force]
Please verify the authentication settings ofcheck your web app and revert it to the previousapplication's authentication provider settings if you see any anomaly.
Reference: https://technet.microsoft.com/en-us/library/gg251985.aspx