This is for info only, and applies to people who are made redundant from their job in Gibraltar, but who live in Spain, in my case, La Linea de la Concepcion - I do not claim to be an expert on the subject this is just my experience of it.
Your HR Dept should give you all relevant forms for taking to the Social Security Dept/ Tax Office in Gibraltar.
You cannot claim any Unemployment benefit from Gibraltar unless you actually LIVE in Gibraltar (despite the fact that you have paid into their Social Security fund) You must claim in Spain, but you can only claim if you are registered in Spain and have an NIE Number.You must have worked in Gibraltar for at least 2 years to be able to claim and you need to have a Spanish Bank Account to have the benefits paid into, they will not accept a Gib or UK account.If you haven't already got a Spanish Account, open one as soon as possible.
Once you have the relevant paperwork signed in Gibraltar, you have to go the Unemployment Office in Spain, this is made harder if you don't speak Spanish as at the Office in La Linea,(near the main Mercadona) I think one person speaks a bit of English only. You will fill in more forms and then make an appointment to return, they will want to see proof of ID, NIE and passport, NIE is not proof that you actually reside in Spain, they will want to see Rent receipts or Rent contract that you have lived in Spain plus utility bills, photocopy it all and take everything with you!
When and if your claim is accepted, you will receive a letter telling you what you are entitled to and how long you will recive benefits for, (obviously it's all in Spanish and you usually have to sign for the letter) it will take about 3 months before you actually recieve any money and it always goes into the Bank on the 10th of the month, unless the 10th falls on a weekend, then it will go in on the next working day.
One massive misconception is that you will receive 70% of whatever salary you were earning in Gibraltar, WRONG! The most anyone will receive, no matter whether you were earning 17K or 100K is 1020 Euros per month, that is the maximum Spanish Social Security payment anyone gets and from this they deduct money for Health Care or Tax (I think) so you will actually get around 988 Euros a month. After 6 payments, this is reduced by 30%. You can normally claim for about 18 months, not sure what happens after that if you still don't have a job.
You sign on every 3 months, its not like signing-on in the UK, they don't want to see proof of all the jobs you've applied for or ask you what you have done to look for work, its just a case of them stamping your card and giving you a new date to attend in 3 months time.
You should also apply for a Tax Rebate in Gibraltar but for some innane reason, even though the Tax Office will know you live in Spain and are no longer working in Gibraltar and therefore have 'left' Gibraltar, they will not accept an address in Spain to send your Tax Rebate, therfore, give them a UK address. (Personally, I was under the impression that if you don't work the complete Tax Year you get all your Tax paid for that year refunded as you did when you left the UK, but despite paying over 5K in tax, I got back less than £200! I disputed it, but they insist its correct)
As I said, I don't claim to be an expert on this subject, but from personal experience, I found it very difficult - if not impossible to find any practical info on this subject.