How can a person make up for days they missed fasting in Ramadan, without knowing their exact number and without possessing money for expiation?

You must immediately make up for any missed days of Ramadan (definition), even if you are unable to perform the expiation (kaffarah (definition)), for the expiation is valid before, during, or after making up the fast. Expiation is required for anyone who delays making up the fast until the next Ramadan begins without a valid excuse. It is not waived due to inability; rather, it remains a debt owed. Inability to perform the expiation does not justify delaying the make-up fast. If you are unsure of the number of days, continue making up the fast until you are reasonably certain that you have fulfilled your obligation, because the obligation is not cleared except with certainty.