Inclusion Criteria:

1. Age between 18 and 80 years.
2. Patients with decompensated cirrhosis admitted to hospital due to AD according to the EASL-CLIF criteria (rapid onset of ascites, hepatic encephalopathy, portal hypertensive-related gastrointestinal bleeding, bacterial infection, or any combination of these).
3. CLIF-C AD score ≥ 45 at admission or at any time during hospital stay.
4. Recovery from AD and expected to be discharged within the next 72 hours.

Exclusion Criteria:

1. Diagnosis of acute-on-chronic liver failure (ACLF) grade 3 or higher according to the EASL-CLIF criteria at admission or at any time during the index hospitalization
2. Admission for planned diagnostic or therapeutic procedures
3. Recent acute bleeding (unless the cause has been effectively treated and there is no evidence of ongoing bleeding for at least 5 days)
4. Chronic bleeding requiring periodic blood transfusions
5. Presence of an ongoing acute complication of the disease (i.e. hepatic encephalopathy [grade III or IV])
6. Conditions with a high risk of haemorrhage, including haemorrhagic diathesis not related to liver disease
7. Patients with INR > 3.0
8. Severe thrombocytopenia (<30x10 9 /L)
9. Ongoing chronic anticoagulation therapy or indication for starting anticoagulation due to hepatic and non-hepatic conditions
10. Ongoing anti-platelets therapy.
11. Active malignancy (except for hepatocellular carcinoma within the Milan criteria or non-melanocytic skin cancer)
12. Antiviral treatment for hepatitis C, B and delta initiated in the last 6 months or planned to be initiated in the following 6 months
13. Ongoing alcohol use disorder with an expected low adherence to protocol as judged by physician
14. Previous liver transplantation
15. Patients with TIPS or other surgical porto-caval shunts
16. Chronic organic renal failure stage IV and V or estimated Glomerular Filtration Rate <30 ml/min according to the MDRD equations
17. Chronic heart failure NYHA class III or IV
18. Pulmonary disease GOLD III or IV
19. Patients with extrahepatic diseases with life expectancy <6 months
20. Severe psychiatric disorders
21. Hypersensitivity to albumin preparations or to any of the excipients.
22. Hypersensitivity to enoxaparin sodium, heparin or its derivatives, including other low molecular weight heparins (LMWH) or to any of the excipients
23. History of immune mediated heparin-induced thrombocytopenia (HIT) within the past 100 days or in the presence of circulating antibodies
24. Pregnancy and breast-feeding
25. Expected low adherence to study protocol as judged by physician
26. Patients who can't provide written informed consent or refusal to participate
27. Participation in other concurrent clinical trials and within the prior 3 months from informed consent signature.