What you describe are ownership issues. These are orthogonal (i.e. independent, you can have either without the other or even both) to object orientation. You have the same issues if you do not use OOP and juggle pointers to POD structs. You don't have the issue if you use OOP but solve it somehow. You can (try to) solve it using more OOP or in another way.
They are also orthogonal to the use of pointers (unless you nit pick and extend the definition of pointer). For example, the same issues arise if two separate places hold indices into an array and mutate, resize and ultimately delete the array.
In C++, the usual solution is to select the right smart pointer type (e.g. return a shared pointer when you wish to share the object, or a unique pointer to signify exclusive ownership), along with extensive documentation. Actually, the latter is a key ingredient in any language.
One OOP-related thing you can do to help this is encapsulation (of course, you can have encaptulation just fine without OOP). For instance, don't expose the object at all, only expose methods which query the object under the hood. Or don't expose raw pointers, only expose smart pointers.