Can a Field class from Java reflection work on any object?

I am curious if I can store an instance of a Field object and use that on any object I pass to it. I'm doing a ton of reflection work, and I recall reading somewhere that it is unsafe to store a Field object and use that as a singleton (more or less) to quickly access the field from the class.

Is this actually possible, or is what I'm trying to do dangerous or flawed in anyway? I made a quick test to check, and it appears to work... but I'm unsure if this test alone actually proves that.

This assumes we're allowed to access the field and a SecurityException won't be raised.

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Code used to test:

package test;

import java.lang.reflect.Field;

public class TestClass {

    public static void main(String[] args) {
        Field fa = null;
        Field fb = null;

        for (Field f : Test.class.getDeclaredFields()) {
            switch (f.getName()) {
            case "a":
                fa = f;
                break;
            case "b":
                fb = f;
                break;
            }
        }

        fa.setAccessible(true);
        fb.setAccessible(true);

        Test ta = new Test(5, "test");      
        Test tb = new Test(54, "new string");

        try {
            System.out.println(fa.get(ta) + " " + fa.get(tb) + " " + fb.get(ta) + " " + fb.get(tb));
        } catch (IllegalArgumentException | IllegalAccessException e) {
            e.printStackTrace();
        }
    }
}

@SuppressWarnings("unused")
class Test {

    private int a;
    private String b;

    public Test(int a, String b) {
        this.a = a;
        this.b = b;
    }
}

Yields:

5 54 test new string