You can reduce the $MP= \{\langle M,w \rangle : w \in L(M)\}$ to $NeverHalt$

For a given string $\langle M,w \rangle $ you construct the following machine $F$:

    For input x:
      Simulate M for input w
        if it accepts, loop
        if it rejects accept x

Now you can see that $\langle M,w \rangle  \in MP \iff  \langle F \rangle  \in NeverHalt$