How do companies and the government afford to pay people a pension?
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There are strict laws when you sponsor a pension plan in most regions requiring you to fund this pension in advance. Those funds become separate and are not allowed to be used by the sponsor later.
Periodically (often, but not always annually) the pension plan is required to submit a report of their assets and their expected payments and make up for any shortfalls.
This was much easier to fund when interest rates were higher than they are today. Due to this, many plans have adjusted the structure of their payments, and instead of getting a fixed guaranteed payment, you’ll find more and more plans offering a fixed contribution (e.g. matching your contributions or a percentage of your salary) and converting that into an annuity when you retire.
Government pensions are a little different. Because governments can issue debt indefinitely or print money as desired, some countries do not set aside funds in advance and just pay out of the general budget.
Canada for example, has both in place.
Canada Pension Plan is paid for with contributions from workers, their employers and investment returns on that money. (Costs are also lower than standard pensions because they are allowed to do things standard pension plans are not allowed to do).
Old Age Security is paid for out of the budget with tax revenues.
Functionally, both of these are pensions.
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