Same issue, "Hazel has been stopped", HazelHelper doesn't get installed to run. Hazel 5.0.1 on Mojave 10.14.6, upgraded from most recent Hazel 4 release.
Clicking the "Start Hazel" button in the error banner produces this console error from the Hazel process:
27366555: RECEIVED OUT-OF-SEQUENCE NOTIFICATION: 0 vs 234, 513, <private>
And this error from the lsd process:
Non-fatal error enumerating at <private>, continuing: Error Domain=NSCocoaErrorDomain Code=260 "The file “PlugIns” couldn’t be opened because there is no such file." UserInfo={NSURL=PlugIns/ -- file:///Applications/Utilities/Hazel.app/Contents/Library/LoginItems/86Z3GCJ4MF.com.noodlesoft.HazelHelper.app/Contents/, NSFilePath=/Applications/Utilities/Hazel.app/Contents/Library/LoginItems/86Z3GCJ4MF.com.noodlesoft.HazelHelper.app/Contents/PlugIns, NSUnderlyingError=0x7fea8d7aa7c0 {Error Domain=NSPOSIXErrorDomain Code=2 "No such file or directory"}}
Removing the broken "HazelHelper" Login Item and manually adding "86Z3GCJ4MF.com.noodlesoft.HazelHelper.app" causes it to show in the menu bar as normal, and rules are being parsed, but not acted on. Selecting the "Run Rules Now" menu item causes the HazelHelper process to crash with this error series:
default 20:00:23.901159 -0800 distnoted register name: com.noodlesoft.Hazel.evalExpiredNotification object: com.noodlesoft.HazelHelper token: f435f pid: 854
default 20:00:24.279592 -0800 Hazel Could not find image named 'info'.
default 20:00:24.905763 -0800 distnoted register name: com.noodlesoft.Hazel.helperLaunch object: com.noodlesoft.HazelHelper token: f44ef pid: 854
default 20:00:24.905887 -0800 distnoted register name: com.noodlesoft.Hazel.helperReady object: com.noodlesoft.HazelHelper token: f44f0 pid: 854
default 20:00:24.928300 -0800 lsd Non-fatal error enumerating at <private>, continuing: Error Domain=NSCocoaErrorDomain Code=260 "The file “PlugIns” couldn’t be opened because there is no such file." UserInfo={NSURL=PlugIns/ -- file:///Applications/Utilities/Hazel.app/Contents/Library/LoginItems/86Z3GCJ4MF.com.noodlesoft.HazelHelper.app/Contents/, NSFilePath=/Applications/Utilities/Hazel.app/Contents/Library/LoginItems/86Z3GCJ4MF.com.noodlesoft.HazelHelper.app/Contents/PlugIns, NSUnderlyingError=0x7ffc6fdcf780 {Error Domain=NSPOSIXErrorDomain Code=2 "No such file or directory"}}
default 20:00:25.180999 -0800 distnoted register name: com.noodlesoft.Hazel.interactiveUpdateCheckCompletedNotification object: com.noodlesoft.HazelHelper token: f44f1 pid: 854
default 20:00:25.181225 -0800 distnoted register name: com.noodlesoft.Hazel.schedulerDidStartNotification object: kCFNotificationAnyObject token: f44f2 pid: 854
default 20:00:25.181338 -0800 distnoted register name: com.noodlesoft.Hazel.schedulerDidStopNotification object: kCFNotificationAnyObject token: f44f3 pid: 854
default 20:00:25.725220 -0800 hazelworker UNIX error exception: 17
default 20:00:25.746247 -0800 hazelworker UNIX error exception: 17
default 20:00:25.751734 -0800 hazelworker UNIX error exception: 17
default 20:00:25.757731 -0800 hazelworker UNIX error exception: 17
default 20:00:25.886317 -0800 loginwindow -[PersistentAppsSupport applicationQuit:] | for app:HazelHelper, _appTrackingState = 2