If it happened suddenly, there would be no life left.
Quoting Dr. Sten Odenwald:
If the Earth stopped spinning suddenly, the atmosphere would still be in motion with the Earth's original 1100 mile per hour rotation speed at the equator. All of the land masses would be scoured clean of anything not attached to bedrock. This means rocks, topsoil, trees, buildings, your pet dog, and so on, would be swept away into the atmosphere.
If the Earth stopped rotating, it's magnetic field would no longer be regenerated and it would decay away to some low, residual value due to the very small component which is 'fossilized' in its iron-rich rocks. [...] This is a significant biohazard.
There's also to consider the change in temperature, having 6 months of day and 6 months of night. On Earth we currently see that only in the polar regions. Life still exists in those areas, especially marine life.
One important note: their climate depends not only on the 6 months light cycle, but also on their angle relative to the sunlight. That's to say that not all Earth would look like that.
Quoting Dr Karl Kruszelnicki:
Life could continue in a narrow twilight zone between the hot and cold halves. But this twilight zone would slowly creep around the planet over the period of a year, as the Earth did its annual orbit around the Sun.
The liquid water in the oceans is far more mobile and responsive to forces. So the Earth's spin has pushed up this liquid water to an 'abnormal' elevation of about eight kilometres. [...] So take away the spin and you take away all water at the equator. [...] The water that left the equatorial regions would have to go somewhere, and that 'somewhere' would be the poles. There would be two totally disconnected polar oceans on each side of the equatorial mega-continent.
All of this points to a very bad scenario for life on earth. The change, being so sudden, would kill pretty much everything.
If Earth gradually slowed down to a halt, over billions of years, then life has a chance. Animals could migrate over million of years and life in general would evolve to survive these changes. Temperatures would still be an issue, especially in the 6 months of day, but underground cave systems and oceans would likely still have plenty of life, being a safe refuge from the extreme temperatures of the surface.
EDIT: Added quote sources:
EDIT 2: As pointed out in the comments, for forgot a pretty important point: if Earth didn't have a magnetic field anymore, we would lose our main source of shielding from radiation. As a secondary effect, the Earth's atmosphere would probably be gone too, although I'm not sure how long this would take. For more info about that, I suggest checking out this article and its sources: https://whatifshow.com/what-if-earths-magnetic-field-disappeared/
I still believe it would be possible for some form of life to survive in closed cave systems, but that's my own hypothesis and I don't have any data to support it.
EDIT 3: Clarification: as pointed out in the comments, life wouldn't be completely gone. Major life forms would, but microbial life might still survive; stuff like bacteria and such can be found very deep underground, and might not be affected in a significant manner by this change.