There is no "input field", the UI state is entirely on your end :).
This is immediate mode UI. It handles inputs and renders simultaneously. Consider a line from the example in the README:
nk_slider_float(&ctx, 0, &value, 1.0f, 0.1f);
That line is responsible for both drawing the slider (at a place determined by value, with min = 0, max = 1, step = 0.1)
and setting the variable `value` to whatever position user is currently dragging the slider to.
Or:
if (nk_button_label(&ctx, "button")) {
/* event handling */
}
That
simultaneously draws the button
and executes the conditional if the button was just pressed.
Immediate mode GUIs are used in games, where you think in terms of drawing frames, each visible for a fraction of a second. When using such GUI, you usually "clear" it at the beginning of the frame, feed it with input from current frame, then build up the UI at the same time as you're drawing it[0].
So basically, you're in total control of the state; there is no persistent "input field", you recreate it each frame with a function call, and it's up to you whether or not it's meaningfully the same input field as it was the last frame.
--
[0] - most times, like in this case, "drawing" means you "build up" a list of display commands which then you feed to the renderer at the end - this lets an immediate mode GUI be independent of whatever graphics library you're using.