"Cadged" is a word that means to beg or ask for something in a persistently annoying way. If you want to use a synonym for "cadged," there are plenty of options available to you. "Begged" is an obvious choice, while "pleaded," "implored," or "beseeched" can be used to emphasize the desperation of the situation. Alternatively, you could use "sponged" or "mooched" to imply that the person was taking advantage of others. And if you're looking for a more formal or sophisticated word, "solicited" or "entreated" might be perfect. Whatever the word you choose, it will help you to create a richer and more nuanced meaning in your writing.