Instead of lecturing me on terminology, can you explain what app, profile, or iOS bug has the ability to remove a search engine option and change this setting against my will? This is a security issue, not a vocabulary test.
The answer to that question is nothing on an iPhone is changed against your will. If you require an answer you will need to rephrase that question.
A Profile, for example, could explain the unexpected addition and equally unexpected deletion of an unwanted Search Engine, but a Profile is not installed against one's will. Doing so requires a deliberate action on the part of the iPhone's owner or authorized user.
Since its title and question amount to gratuitous assertions I suggest you start a new one, and I also suggest you post it in the iPhone Community. This is not a Safari question for the reasons already explained.