Short answer
Do not buy eggs with cracked shells. If an egg cracks accidentally during handling at home, transfer it immediately to a clean covered container, refrigerate and use promptly in a thoroughly cooked dish.
Why the shell matters
The shell and membranes form a physical barrier. A crack creates a route for surface bacteria and allows contents to leak. The longer the history is unknown, the less sensible it is to keep the egg.
Different cracking situations
An egg already cracked in a retail carton should be rejected. An egg that cracks during hard boiling can be safe when thoroughly cooked. If it cracks cleanly on the journey home, separate and chill it promptly; discard it if dirty, leaking or left warm.
Do not save pooled eggs casually
Cracking several eggs together increases the consequence of one contaminated egg and makes storage history harder to track. For advance preparation, use pasteurised liquid egg or follow a validated professional procedure rather than keeping an uncovered bowl.