Here's how it works: you fill out your annual income tax return, you answer a question about health insurance, if you didn't have it and you don't qualify for an exemption then you owe the tax office the value of the penalty in addition to your other tax contributions.
Don't file an income tax return? Then you don't have to pay the tax penalty.
Even if you do file a tax return, there are exemptions. For example if there is no plan on your local exchange costing less than 8% of your income then you are not required to pay the penalty.
Will the police come after you if you don't pay it? No, but the IRS will remember and take the money from any future tax returns.
In general you won't get in trouble for not paying taxes. Something like 7M Americans fail to pay their taxes every year and the IRS only investigates 100k or so. Even if the IRS does audit you, they rarely press charges.
In conclusion: If you're poor, then you probably don't have to pay the penalty. If you do have to pay, but don't feel like it then go ahead. No one is going to throw you in prison, police will not be involved. The IRS will probably just take the money from you when they get a chance.
The answers to your questions are here: https://www.healthcare.gov/fees-exemptions/fee-for-not-being-covered/