In general, it is important to see, that most of psychological problems do not only have dysfuctional elements to them, but also functional elements.
For example, being depressed might encourage people important to us, to care for us.
Avoiding situations due to anxiety might keep us from stressful moments.
Due to the fact that most forms of "not feeling well" have some rewarding or stabilizing elements to them, it is understandable to some degree, when people say that a part of them "does not want to get better".
However, it is essential to note that the positive consequences of certain psychological issues are usually short term - and they come with negative long term consequences.
In the example above, your boyfriend might treat you more carefully or care for you if you are depressed (Positive short-term consequence). However, the constant pressure on the relationship due to the depressed mood might lead to arguments or a break-up as well (long-term negative consequences).
Before you are sure, if you really do not want to get better, it is important to carefully evaluate the short term and long term consequences of your current situation.
Finally, you have to ask yourself the question: What kind of life do I want to live? Your answer might be, that you want to live on exactly as you are doing right now (i.e. not feeling well). This decision is personal. No one eles is to say if it is "normal" or not.