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 $\langle M,w \rangle \in MP \iff \langle F \rangle \in NeverHalt$