Plenty of good investments are insured. There are whole classes of investment that simply would not be sane to do without insurance. Taking an example from every day life: People buy investment properties and most of the time they insure them.
If you want something more financial a short vertical spread [0] is a strategy in which you are purchasing insurance on the risk (investment) you just took (made). There are many such investments of this form.
[0] https://www.optionsplaybook.com/option-strategies/short-call...
Perhaps you're thinking of a collar? (short calls to fund puts?)
A short call spread is someone selling calls (option A in the link) and buying insurance on said sale (option B in the link).