The problems faced by citizens of a non-democratic country are considerable, and sometimes fatal.
"Non-democratic," by definition, implies an autocratic or dictatorial form of government, such as existed in the Soviet Union and across Eastern Europe during the Cold War, and in countries like North Korea, Venezuela and Cuba today. (For purposes of discussion, I'll omit war-torn quasi- or non-democratic governments in Iraq, Syria and Afghanistan.) In countries ruled by dictators, either a political party like the Communist Party of China or by individuals like the late Fidel Castro in Cuba or the ruling Kim family in North Korea, the people can either submit to all forms of oppression, or suffer the consequences of dissidence—real or perceived—by being thrown into brutal prison camps and tortured and starved to death, or by being summarily executed with a bullet to the back of the head.
Dictatorships deny their citizens the fundamental freedoms Americans and others in democratic countries take for granted, such as the freedoms of speech, assembly, and religion. They deny their citizens due process of law, and provide extremely limited opportunities for professional careers. In some non-democratic countries, like Chile under the late Augusto Pinoche and, since the late 1970s, China, there is a large measure of economic freedom (although, in China, most major corporations are owned by the state and, in effect, by the Chinese Communist Party and the People's Liberation Army). In most non-democratic countries, however, the government maintains strict controls on the economy, and many people spend their lives essentially slaving away in government-controlled factories, working for minimal wages and little or no benefits.
Another problem of non-democratic countries is the prevalence of corruption. Although present in democracies, dictatorships virtually always exhibit extraordinarily high levels of official corruption. Bribes for basic services are a way of life, and judicial systems are similarly corrupt, with bribes needed to ensure a favorable outcome. Police are routinely bribed and many such police departments engage in criminal conduct themselves, such as extortion of businesses and individuals in order to for the latter to be "free" to operate.
Finally, as bad as the environment in many democracies has become, the situations in dictatorships are even worse—much worse. Environmental degradation associated with the nuclear weapons complex in the United States was revealed, after the Cold War, as far worse than many understood. In Russia and the former Soviet republics, the conditions were beyond imagination. As badly as manufacturing plants in America polluted waterways, the situation in countries like Russia and China is far worse, because there has been little or no freedom to protest those conditions, as the media are controlled by the governments and the freedom to protest is strongly denied. Whistle-blowers and human rights activists regularly risk their lives in such countries, not just their jobs. Investigative journalists in democratic countries may, at worst, be jailed for their refusal to disclose their sources of classified information, and such cases are very rare (most prominent examples in the U.S. occurred during the Obama Administration). In Russia, one of the deadliest professions is that of investigative journalist. Russian President Vladimir Putin's enemies in the press and elsewhere have a tendency to end up dead.
The first problem faced by a non-democratic country is lack of civic involvement. Because people have no say in government, they are less likely to be engaged in civic activities, other than what is necessary to curry favor with those in power. If citizens resent their lack of freedom and lack of voice in government, the country can become a breeding ground for insurgencies. Such political instability can discourage long term investing, and especially foreign investment.
Next, if the government is corrupt or incompetent, the only way to replace it is through armed revolution. There are no checks and balances in place to keep such governments honest. Although a non-democratic country can be lucky in having just and good rulers, there is no way to ensure that such luck continues. Succession crises can also be a problem.
Finally, lack of freedom affects quality of life for the residents of the country.