It is possible to combine a reflector and a refractor telescope together? I know it sounds crazy, but is it possible to 
connect a reflector telescope and a refractor telescopes (like monocular for bird watching) together to build a better telescope?
...is it possible to connect a reflector telescope and a refractor telescopes (like monocular for bird watching) together...

Yes, a properly focused telescope (for someone who's not near-sighted) will have infinity conjugate focal points; parallel rays in make parallel rays out.
If the telescope is set up for 50x magnification (f=600 mm objective, f=12 mm eyepiece) then a 1 degree field of view (FOV) in the sky will be a 50 degree apparent FOV at the output of the first eyepiece.
Alas, a second 8 x bird-watching monocular may only have a 7 degree input FOV so we will indeed get 50 x 8 = 400x magnification, but of a 0.14 degree field.
That's just what you would get looking through a single telescope set up for 400x (say f=1200 mm objective, 2x Barlow and f=6 mm eyepiece).
In other words, you could do this, but...

...to build a better telescope?

I'm not sure it would be better in any possible way if it's for looking through.
However, if you have an old CMOS imager webcam from the 1990's with giant pixels and you want to blow up the primary focal plane of the first telescope to get some useful resolution, this might be a suboptimal solution. You could remove the eyepiece of the second bird-watching monocular and put the image sensor with too-large pixel size there and get better resolution than if you'd put it at the focal plane of the first telescope.
A better way to solve this unlikely problem might be to simply use positive or eyepiece projection with the first telescope's eyepiece moved outwards so that it's final focal point moves in from infinity to say roughly 8 times its focal length.
That would have the same effect but without adding the monocular.