For example, let's say I'm editing an object and I reach a field that needs certain data. But the data is elsewhere in the app. Rather than abandoning my changes, I would prefer for the app to save my changes so I can later return to the object, fill in the data, and hit Save. Has anyone seen this kind of functionality on a phone?
It sounds like you may need a picker, if the information the user would fish for is structured (date, file, contact, order#, etc.)
The most common types of pickers are dates, files, time, but you can create your own custom picker for your own data type and flow. This is particularly important for complex information in a large information space, like picking a contact in a phonebook, where you might want to help users select by first name, last name, or even add a filter / search feature.
Examples of pickers:
jQuery UI: https://jqueryui.com/datepicker/
jquery plugin image picker: http://rvera.github.io/image-picker/