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

For a given string $<M,w>$ you construct the following machine:

F: "For input x:

1.Simulate M for input w
if it accepts, loop
if it rejects accept x "

Now you can see that $<M,w> \in MP \iff <F> \in NeverHalt$

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