In proportional representation, single-party majority governments can still form - as long as an actual majority of the voters truly supports them.
A more common outcome, however, is majority coalition governments - made up of a combination of different parties, none of whom have earned a majority in their own right. In these systems, parties to *learn* to get along and negotiate with each other to make progress.
Here is a list of countries that currently operate with coalition governments: https://en.wikipedia.org/wiki/List_of_countries_with_coalition_governments
With at least 2 parties needing to agree on every bill, there’s less chance of any single party is pushing its own agenda or acting unfairly, because there is a built-in check-and-balance. Under First Past the Post, a party can put policies in place without the support of a majority of the population. Then, when the government changes to the other colour in a few elections time, their first year in government is often spent undoing the worst policies that the previous government put in place.
Countries with Proportional Representation actually tend to have more stable long-term policies than those with First Past the Post, and legislation is better-considered before being passed.
No one likes unstable governments, and under the First-Past-The-Post system, minority governments are indeed unstable, because minority governments will readily dissolve and call a fresh election, knowing that they have a good chance of winning a 'false majority'.
One of the great things that we see in countries with proportional representation is that there is actually more stability, and less frequent elections, because minority governments won't voluntarily dissolve - they know that there's very little chance of them winning an unfair majority!
Here is a great opinion piece from island publisher Paul MacNeill, addressing the 'suspect definition of stability' that seems to be held by many defenders of the current, First-Past-the-Post system: http://www.peicanada.com/eastern_graphic/article_0f5408b0-a065-11e6-a21d-3be2ed981b44.html