I hope that no other rats become affected. If one does, I wonder if your vet would consider a long-shot treatment?
If the cause of the bleeding turns out to be warfarin, maybe orally-provided Vitamin K would work. Evidently that works for humans. Warfarin "thins" the blood by interfering with Vitamin K, which is necessary for production of the blood clotting factors.
Here's what I found on a web site about using Vit K as an antidote to too much warfarin: injections of Vit K and "pigging out" on shrimp. Web site is
http://www.flounder.com/warfarin.htm
"Warfarin was used in the 1950s as an anticoagulant for victims of heart attacks and strokes, but gained fame when it was used to treat President Dwight D. Eisenhower after his 1956 coronary (while in office).
Therapeutic doses of warfarin are minuscule: 2mg to 10mg for a 100kg person. The actual dosage depends upon an individual's diet and metabolism, as well as body weight. In fact, body weight is not a major factor. A 150kg person may require 2mg while a 75kg person may require 10mg for the same therapeutic effect.
There are very few good alternatives to sodium warfarin treatment. In some cases, a doctor may prescribe low-molecular-weight heparin (LMWH). I do not know the issues about long-term effectiveness of LMWH, but the fact that it requires two injections per day, subcutaneous, at fairly precise 12-hour intervals, precludes its use for most people. I've done it in the short-term (post-surgical recovery while the warfarin is "ramping up"). I wouldn't want to have to do it every day.
Warfarin impairs the creation of one of the significant blood clotting factors, prothrombin. Vitamin K is an important factor in the synthesis of prothrombin clotting factors in the blood. Because of this, Vitamin K is considered an "antidote" for warfarin overdose.
If a child or pet inadvertently consumes a warfarin-based rodenticide, the usual treatment is injections of Vitamin K. This is simplified greatly because the actual effects of the warfarin can be measured fairly accurately by measuring the blood clotting rate. This "prothrombin clotting time" or "protime" measurement is necessary for anyone on warfarin prophylaxis therapy. Tests may be done as frequently as daily to as infrequently as monthly.
The complementary problem for people on warfarin therapy is that it is necessary to keep a balanced intake of Vitamin K.
Many foods are high in Vitamin K, including shrimp and spinach, and an unbalanced intake of Vitamin K will cause the prothrombin times to vary wildly. This is not to say that foods containing Vitamin K must be avoided; merely that the intake should be reasonably constant, so the warfarin dosage can be adjusted to compensate for it. For example, an occasional spinach salad is not considered dangerous, but a spinach salad every night for two weeks would not be a good idea, particularly if there was a prothrombin-clotting-time test taken just at the end of those two weeks. Besides the risk that the sustained Vitamin K intake would cause (due to lowered clotting time), an adjustment made to the dosage followed by a discontinuance of the intake would result in a significantly raised clotting time. So the key is to maintain a reasonably constant Vitamin K intake.
When my prothrombin clotting factor (measured in units expressed as the "INR", an acronym for the International Normalized Ratio) goes above a number my doctor and I have agreed upon, I can pig out on shrimp. Below that value, it is not a good idea, and if I drop below another level, it could be seriously dangerous to pig out on shrimp. Note that my physician and I have agreed upon certain values, based upon my medical condition. If you are on, or are using this for someone who is on, anticoagulant therapy, you must consult your physician regarding which values are appropriate. For someone on prophylactic anti-stroke therapy these numbers would be quite different, for example. Consult your physician for your particular case."
From what I read on this web page, it would be great to feed that cage some shrimp and spinach. If anyone is on abs, it would be important to replenish their gut flora with probiotics to prevent further loss of Vit K production.