A title never, in itself, conferred either a right to income or a right to property.
But, if the king was granting you a title to thank you for some conspicuous service to the nation or to himself (winning a battle, acknowledging as your own the king’s bastard child, that kind of thing) he might also grant you land or other valuable rights that were at his disposal.
That practice pretty much died out by the eighteenth century. Thereafter it was usually the case that titles of nobility were only given to people who were already wealthy, and had land. (In fact, this has been the norm even before; even when the king granted property along with a title, the grantees were usually people who were already not short of a few sandwiches.)
Titled families traditionally attempted to conserve their wealth and ensure that it passed with the title (hence the stereotype of the near-penniless “younger son” from an enormously wealthy family). Inevitably, though, over the years many of them have seen their wealth decline whether through bad luck, bad judgment, division between numerous heirs, taxation or some combination of these. Consequently there are many peers who live, in material terms, quite ordinary lives.
For example, the 18th Earl of Lincoln was born in Melbourne in 1913. His father was a sailor in the British merchant navy. He had a relatively privileged education at an independent boarding school in Western Australia, but thereafter worked as a boilermaker, a welder’s assistant and a butcher at a mining camp. He was 76 before he inherited the title from a distant cousin; he had known for many years that he was in line as a possible heir, but had forgotten about it. No money or property came with the title.
Jtur88 suggests, in post #12, that people in this situation might have “just stopped passing the hereditary entitlement down anymore”. In fact, this isn’t an option. If you are the 11th Earl of Littleshit, then your heir is entitled to be the 12th Earl of Littleshit on your death; there is nothing you can do to “stop passing the hereditary entitlement down”; that’s pretty much what “hereditary entitlement” means. But your heir can decide not to use the title, and continue to call himself Joe Bloggs even though he is, in law, the Earl of Littleshit (and in fact this is quite common). And, since 1963, your heir has been free to formally disclaim the title, in which case he isn’t the Earl of Littleshit. But even that won’t stop the title passing down; his heir will be the 13th Earl, unless he, too, decides to disclaim.
Disclaimer is rare; only a few people have formally disclaimed their peerages, and in most or all cases this was done to allow them to sit as members of the House of Commons. Since peers are no longer excluded from the House of Commons the principal reason for disclaiming no longer applies, and in fact nobody has disclaimed a peerage since 2002.