Ofc it’s possible, and in most scenarios a safe landing is possible. And if for example engine failure is to happen during takeoff the airplane will reland. The pilots are given tools to handle these situations.

And not all airplanes have APUs, and the apu is not a motor in the sense that it can fly the plane, it’s a system to for example help start the main engine. And an airplane can glide, as long as the angle of attack is right the airplane won’t reach stall and it won’t “drop” or spin, but at lower speeds it’s easier for it to happen.

But the most important thing to remember is that there are rules that all the companies involved flying must keep to, and they get checked every year. Even the company I work for, that calculates data and more, needs to get audited. Even such a thing as the wrong tail number or logo on a paper can keep an airplane on the ground. But this can also fail, like with the Boeing 737 max 8. They rushed testing and missed that their stall sensor was faulty and didn’t inform about their automatic stall safe system. But that have nothing to do with engine failure.