I don't think "modern philosophers" is a very good translation, it implies something in English that Cicero is not implying in Latin. The passage is from the de Amicitia:

Neque enim assentior iis qui haec nuper disserere coeperunt, cum corporibus simul animos interire atque omnia morte deleri

For neither do I agree with those who recently have begun to argue that the soul dies at the same time as the body and also that death is the end of everything

The Latin that Cicero uses, nuper, is an adverb meaning "recently, just now," and really it shouldn't be attached to the iis qui at all as that gives the wrong sense, although I suppose something like "recent philosophers" might be a tolerable, if odd (since nuper most definitely modifies coeperunt) translation. "Modern philosophers" I think is definitely not right, since "modern philosophy" implies something in English that is not present in the Latin--Cicero just means that the particular people he's talking about have come about recently. He means the Epicureans, who were something of a fad among the Roman elite of Cicero's lifetime. Stoicism, which would be prominent during the Principate, had not really taken hold, and Cicero's own Academism wasn't especially popular among the fashionable. Epicureanism was a relatively new introduction to Roman society--Lucretius' de Rerum Natura had only been published five to ten years before the writing of the de Amicitia. The Epicureans held that the soul was, like the body, atomically-composed and therefore material, and that it would therefore perish at the same time as the material body did. This particular concept of Epicureanism is something that Cicero investigated at several points in his literary career, usually betraying much better knowledge of Epicurean thought than he openly professed to have

Yasssss questions about ancient philosophy !! As u/XenophonTheAthenian already aptly corrected the English translation and pointed out the Epicureans - I thought I could chip in with some more detail (also, I'm trying to avoid doing the actual writing I'm supposed to be doing today...)

Cicero lived in Rome in a time when Greek philosophy was extremely fashionable, and he and many of his peers spent a lot of time in Greece studying not just Epicureanism, Stoicism, and Plato's Academy, but great many other schools and philosophers, too. The Republican Romans rarely learnt and read only about only one school of thought. I think it's a bit difficult to say whether he's referring specifically to the Epicureans, because, technically Epicureanism was not any more '"recent" school of thought in Rome than any other Greek schools were. All Greek philosophical schools arrived at Rome around the same time, and although De Rerum Natura was written just a few years before Cicero, it is also the first known written Latin philosophical work; so, I'm not sure if Cicero would have experienced Epicureanism as a 'recent' fad in contrast to other schools since he himself would have learnt about it already in his youth. I mean, it is possible that he's talking about the followers of Epicurean Philodemus in Pompeii who had become a big thing around the time of writing De Amiticia - but, that would mean that Cicero has made the anachronistic mistake of making Laelius call a group that was not in existence during Laelius' lifetime 'recent'! Laelius and Scipio lived during the Middle Republic. So, I wonder if it's possible that Cicero is, with nuper, referring in general to the 'new' Hellenistic schools, as opposed to the 'old' classical Greek philosophy, e.g. Plato and Aristotle...?

If this is the case, there were a few Hellenistic thinkers and movements that held that there is no after-life, and that human souls, or at least human personalities, do not survive death. Here's a summary of the most notable ones:

1. the Epicureans: they believed that soul, just like matter, simply consisted of atoms and void - the difference between soul and matter was mainly that the atoms of the soul were 'particularly fine' and distributed throughout our bodies. Upon a person's death, this delicate texture of atoms scatters and is dispersed in the universe, where the atoms will eventually form new entities, just like the atoms of the physical body will do more slowly. Therefore, the soul does not survive death and there is no after-life, only nothingness.

2. the Stoics: The Stoics had a bit more complicated view of the soul, and they did not really share a clear conception of afterlife; our ancient Stoic sources give somewhat opposing views. Firstly, Stoics seem to understand soul (logos, sometimes also referred to as pneuma, with somewhat different nuances) as simply the rational function of human beings, i.e. logic, rationality, the ability to self-control, so, the ideas of individuality or personality are not really included. The soul of every human being is a small part of the great logos of the world, the logic that is sometimes called God and which co-ordinates fate and the order of the universe. Some Stoics hold that, upon a persons death, the rational souls returns to this God or logos, perhaps to appear again in a New World; some believed that great souls, 'hardened' by the perfect exercise of using rational functions, could survive death in some form, at least until the next conflagration (this is related to another complicated Stoic view about the cyclical order of universe - Wikipedia seems to have decent basic summaries on Stoic cosmology if you want to follow up). Anyway, it appears that the Stoics did not at least believe in the survival of personalities, i.e. you couldn't die as Cicero and continue to have the self-consciousness of being Cicero.

The Presocratics and the Pythagoreans were actually even older schools than Plato, but they were popularly written about during the Hellenistic and Roman times, with some new contributions during the era. Quintus Sextius, who was active during or shortly after Cicero's lifetime, actually made an attempt of forming a distinctly 'Roman' philosophical school which was a mash-up of Stoicism and Pythagoreanism. Therefore, there's a chance that Cicero would have conceptualised these theories as 'recent' (i.e. Hellenistic), so, I might just as well shortly introduce them, too.

3. The Presocratics: The Presocratic views vary, and they mainly thought that soul, too, was made of the main elements, mainly air (sometimes also fire), and in this respect it was not different from body; so, we might assume that some of them believed that the fate of the soul was the same as that of the body upon death. Some Presocratics, though, believed in some sort of survival and cyclical rebirth of the soul, comparable to Buddhism, although it's very unclear to what extent they believed in the survival of personality. My favourite is Empedocles of Acragas in Sicily who claimed that he used to be a bush in his past life. (As a bonus fact, he also believed that animals, too, had human-like souls made out of air, ergo eating animals would be cannibalism, and thus he advocated vegetarianism!)

4. The Pythagoreans: Pythagoras was known in the ancient world as a 'specialist' at what happens to the soul after death, and he believed in the transmigration of soul similarly to Empedocles, and his theory is known as metempsychosis. It is somewhat unclear whether he believed that this was just a sort of natural order of things, where the souls moved rhythmically from humans to animals and plants without any continuation of personality. There’s a famous Xenaphanes fragment (fr. 7), which might suggest this, though: he reports that “once when he [Pythagoras] was present at the beating of a puppy, he pitied it and said ‘stop, don't keep hitting him, since it is the soul of a man who is dear to me, which I recognized, when I heard it yelping!”.

There are other minor Graeco-Roman philosophers and movements which denied after-life and the survival of souls, but those are the most important ones. Laelius himself in the passage you’ve quoted is advocating the Platonic theory of the soul - the “man who was declared by Apollo's oracle to be ‘most wise’” he is referring to is Socrates, who is the main character in Plato’s influential treatise of the soul, Phaedo.