Hi, I'm Ashik. Welcome to JustAnswer. I'm reviewing your question now, and will post back with your reply ASAP
Do you mean you lost the Safari application from your Mac ?
Could you please explain the issue a little more ?
If you lose the Safari application itself, then click on Finder icon on dock. Then click on Go menu at the top bar and select Applications. You will find Safari application there. You can open it from there. Or just search Safari application on Spotlight (searchbox/magnifier icon at top right of screen) and this will bring Safari. Open it from there.
If you still have Safari but lost the icon for some website, then try the fixes below;
Open Safari application. In Safari application, click on Safari menu at the top left next to Apple menu and select Clear History and Website Data. On the drop down next to Clear, select All History and click Clear History.
(If you see Reset Safari instead, click it and Reset Safari)
Restart Safari and do you see the Login and logout icons now ?
Please let me know if that didn't work, so I will continue to help you
This usually happens if the system files are corrupted. We can run Disk Utility and see if it works or not. Turn off your Mac by holding down Power button for 10 seconds. Then turn it back on and immediately hold down Command and R keys at same time for 20 seconds and this will boot your Mac to the Mac OS X Utilities screen. From there, click Disk Utility. Select your hard disk at left column (Macintosh HD or hard disk name). Then click Verify Disk (under First Aid). If asked to repair, click Repair Disk. Then click Repair Permission.
If you are using latest Mac OS X El Capitan, then you will not see Repair Disk option in Disk Utility. Instead click First Aid button and run it. Repair if asked.
Then restart from Apple menu. If that didn't work, then shut down your Mac from Apple menu. Turn it back on and immediately hold down Command, Option, P and R keys at the same time for 5 seconds, then release the keys and immediately hold down Shift key for 20 seconds. Does it work now ?
Please let me know if that didn't work, so we can continue troubleshooting.