Yes! Demoting is actually a method to fix MMR, this usually only applies if you're gaining around 8-14lp, these numbers would slightly even out to match your LP losses.

Can MMR go up if you lose?

If you forget that you need to play ranked frequently and accidentally decay, your MMR will stay the same even if you end up dropping several divisions. In that situation, your LP gains will be much higher as the game tries to promote you in the division where you belong.

Can MMR be improved?

MMR is a number that increases with each ranked match you win and decreases with every loss. Every Dota 2 player queues for a ranked match to increase his/her MMR and get to the higher levels of the game. A lot of people try their best to increase the MMR but fail.