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@vnp's code is solid and helpful, but his stringify_state_helper is a single-purpose function, and still leaves a degree of repetition and memory management in stringify_state. I'd rather have general-purpose to_string that takes printf-style arguments, allocates sufficient space for the converted result, and prints into that space, and returns the result:

#include <stdio.h>
#include <stdarg.h>
#include <stdlib.h>

char *to_string(char const *fmt, ...) { 
    va_list args;
    va_start(args, fmt);

    va_list args_dupe;
    va_copy(args_dupe, args);

    int size = vsnprintf(NULL, 0, fmt, args);

    char *ret = malloc(size+1);

    if (ret != NULL)
        vsnprintf(ret, size+1, fmt, args_dupe);

    va_end(args);
    va_end(args_dupe);

    return ret;
}

In fairness, this does require a little more code, and the v*printf functions (and argument-list macros) are a bit less known, so some may find it a bit more difficult to understand.

On the other hand, in exchange for that bit of extra investment, we get something that's more general, and works much more as I think most people would expect--for example, something like this:

char *s = to_string("%d, %d", 1, 2);

Using this, stringify_state should turn out something like this:

char* stringify_state(State* state) {
    Pet* p = state->pet;
    Settings* s = state->settings;

    return to_string("%lld %f %f %f %f %f %f %f %f %f %f",
                     state->last_update_time,
                     p->health, 
                     p->max_health, 
                     p->satiation, 
                     p->max_satiation,
                     s->milliseconds_per_tick, 
                     s->hunger_pain_per_tick, 
                     s->hunger_per_tick,
                     s->satiated_heal_per_tick,
                     s->pain_per_wrong_answer,
                     s->satiation_per_right_answer);
}

#Other Points

1. Given the number (and length) of arguments you're passing, I'd prefer to see the arguments passed one per line as I've formatted them above, rather than a variable number per line to justify out to some particular right margin.

2. Since stringify_state isn't intended to modify the state whose address is being passed, it's probably better to define the parameter as a State const *. Likewise with the local variables, so the first lines would probably be better written something like this:

    char* stringify_state(State const* state) {
        Pet const* p = state->pet;
        Settings const* s = state->settings;